1rBTX 02. POLINOMIS/1.2.0 Repàs de polinomis 1.2.0.10DT DIFERÈNCIA DE QUADRATS  

Diferència de quadrats
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨24px¨»«mrow»«mfenced mathcolor=¨#191919¨»«mrow»«mi mathcolor=¨#0000FF¨»a«/mi»«mo»+«/mo»«mi mathcolor=¨#FF0000¨»b«/mi»«/mrow»«/mfenced»«mo mathcolor=¨#191919¨»§#183;«/mo»«mfenced mathcolor=¨#191919¨»«mrow»«mi mathcolor=¨#0000FF¨»a«/mi»«mo»-«/mo»«mi mathcolor=¨#FF0000¨»b«/mi»«/mrow»«/mfenced»«mo mathcolor=¨#191919¨»§#160;«/mo»«mo mathcolor=¨#191919¨»=«/mo»«mo mathcolor=¨#191919¨»§#160;«/mo»«msup mathcolor=¨#191919¨»«mi mathcolor=¨#0000FF¨»a«/mi»«mn»2«/mn»«/msup»«mo mathcolor=¨#191919¨»-«/mo»«msup mathcolor=¨#191919¨»«mi mathcolor=¨#FF0000¨»b«/mi»«mn»2«/mn»«/msup»«/mrow»«/mstyle»«/math»
Exemples:
(4x + 9)(4x - 9) = (4x)2 - (9)2 = 16x2 - 81
(2x3 + 5y)(2x3 - 5y) = (2x3)2 - (5y)2 = 4x6 - 25y2



 
]]> 0.0000000 0.0000000 0 1.2.0.11Q DDQ G1 Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»m_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»m_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math»


]]> 1.0000000 0.5000000 0 0 #s_32 <question><wirisCasSession>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;m_1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;m_2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_32&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;m_1&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;m_2&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;8&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_32&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;49&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;64&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml"> #s_32 </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> (a+b)(a-b) = (a2 - b2)
(#a_1 x + #a_2)(#a_1 x - #a_2) = (#a_1·x)2 - (#a_2)2

]]> 1.2.0.12Q DDQ GAleat Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»m_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»m_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math»


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(#a_1 x + #a_2)(#a_1 x - #a_2) = (#a_1·x#g)2 - (#a_2·x#h)2

]]> 1.2.0.13Q DDQ Frac Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»m_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»m_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math»


]]> 1.0000000 0.5000000 0 0 #s_32 <question><wirisCasSession>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;apply&gt;&lt;csymbol definitionURL=&quot;http://www.wiris.com/XML/csymbol&quot;&gt;repeat&lt;/csymbol&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;b_1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;c_1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mi&gt;b_1&lt;/mi&gt;&lt;mi&gt;c_1&lt;/mi&gt;&lt;/mfrac&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;b_1&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;mod&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;c_1&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;≠&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/apply&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;apply&gt;&lt;csymbol definitionURL=&quot;http://www.wiris.com/XML/csymbol&quot;&gt;repeat&lt;/csymbol&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;b_2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;c_2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mi&gt;b_2&lt;/mi&gt;&lt;mi&gt;c_2&lt;/mi&gt;&lt;/mfrac&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;b_2&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;mod&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;c_2&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;≠&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/apply&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;m_1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;m_2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_32&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mfenced&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;/mfenced&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;msup&gt;&lt;mfenced&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;/mfenced&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mfrac&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;m_1&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mfrac&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mfrac&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;m_2&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mfrac&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mfrac&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_32&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mfrac&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;/mfrac&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;25&lt;/mn&gt;&lt;mn&gt;121&lt;/mn&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml"> #s_32 </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> (a+b)(a-b) = (a2 - b2)
(#a_1 x + #a_2)(#a_1 x - #a_2) = (#a_1)2 - (#a_2)2

]]> 1.2.0.14Q DiferènciaQuadratsxy Calcula (#a_1 x + #a_2 y)(#a_1 x - #a_2 y)

]]> És (#a_1 x)2 - (#a_2 y)2

]]> 1.0000000 0.5000000 0 0 #s_32 <question><wirisCasSession>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_32&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mfenced&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;/mfenced&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;msup&gt;&lt;mfenced&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;/mfenced&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;10&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_32&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;100&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;16&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml">#s_32</correctAnswer></correctAnswers><localData><data name="inputField">textField</data></localData></question> 1.2.0.15Q DiferènciaQuadratsx^n,y^m Calcula (#a_1 x#n + #a_2 y#m)(#a_1 x#n - #a_2 y#m)

]]> És (#a_1 x#n)2 - (#a_2 y#m)2

]]> 1.0000000 0.5000000 0 0 #s_32 <question><wirisCasSession>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;apply&gt;&lt;csymbol definitionURL=&quot;http://www.wiris.com/XML/csymbol&quot;&gt;repeat&lt;/csymbol&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd/&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;&amp;gt;&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/apply&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_32&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mfenced&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;/mfenced&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;msup&gt;&lt;mfenced&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;/mfenced&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_32&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;25&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;10&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml">#s_32</correctAnswer></correctAnswers><localData><data name="inputField">textField</data></localData></question> 1.2.0.20DT QUADRAT D'UNA SUMA/DIFERÈNCIA  

Quadrat d'una suma/diferència

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨24px¨»«mrow»«msup»«mfenced»«mrow»«mi mathvariant=¨normal¨ mathcolor=¨#0000FF¨»a«/mi»«mo»+«/mo»«mi mathvariant=¨normal¨ mathcolor=¨#FF0000¨»b«/mi»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«mo»=«/mo»«msup»«mi mathvariant=¨normal¨ mathcolor=¨#0000FF¨»a«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»2«/mn»«mo»§#183;«/mo»«mi mathvariant=¨normal¨ mathcolor=¨#0000FF¨»a«/mi»«mo»§#183;«/mo»«mi mathvariant=¨normal¨ mathcolor=¨#FF0000¨»b«/mi»«mo»+«/mo»«msup»«mi mathvariant=¨normal¨ mathcolor=¨#FF0000¨»b«/mi»«mn»2«/mn»«/msup»«/mrow»«/mstyle»«/math»
Exemple:
(4x + 9)2 = (4x)2 + 2·4x·9 + (9)2 = 16x2 + 72x + 81
Però si és una diferència: 
(4x – 9)2 = (4x + (-9))2 =   16x2 – 72x + 81



 
]]> 0.0000000 0.0000000 0 1.2.0.211Q QuadratSuma Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»m«/mi»«msup mathcolor=¨#003300¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«/mstyle»«/math»


]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>11</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>11</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>A</mi><mo>+</mo><mi>B</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msup><mi>m</mi><mn>2</mn></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>60</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>36</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> (A + B)2 = A2 + 2·A·B + B2

 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#0000FF¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msup mathcolor=¨#0000FF¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»A«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»A«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»B«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msup mathcolor=¨#0000FF¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»B«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/math»

 

 

 

]]> 1.2.0.212Q QuadratSumaG1G0_2 Calcula (#m)2

]]> Es calcula amb (#a_1 x)2 + 2·(#a_1 x)·(#a_2) + (#a_2)2

]]> 1.0000000 0.5000000 0 0 #s_32 <question><wirisCasSession>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_32&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_32&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;81&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;126&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;49&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml">#s_32</correctAnswer></correctAnswers><localData><data name="inputField">textField</data></localData></question> 1.2.0.213Q QuadratSumaGsup1G0 Calcula (#m)2

]]> Es calcula amb (#a_1 x#n)2 + 2·(#a_1 x#n)·(#a_2) + (#a_2)2

]]> 1.0000000 0.5000000 0 0 #s_32 <question><wirisCasSession>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_32&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_32&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;25&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;8&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;30&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml">#s_32</correctAnswer></correctAnswers><localData><data name="inputField">textField</data></localData></question> 1.2.0.214Q QuadratSuma Fracció Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»m«/mi»«msup mathcolor=¨#003300¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«/mstyle»«/math»


]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>11</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>c_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>11</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_1</mi><mo>=</mo><mfrac><mi>b_1</mi><mi>c_1</mi></mfrac></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>b_1</mi><mo>&nbsp;</mo><mi>mod</mi><mo>&nbsp;</mo><mi>c_1</mi></mrow></mfenced><mo>&ne;</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>11</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>c_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>11</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mfrac><mi>b_2</mi><mi>c_2</mi></mfrac></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>b_1</mi><mo>&nbsp;</mo><mi>mod</mi><mo>&nbsp;</mo><mi>c_1</mi></mrow></mfenced><mo>&ne;</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>a_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>(</mo><mi>a_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_2</mi><msup><mo>)</mo><mn>2</mn></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>11</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mfrac><mn>11</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>9</mn><mn>4</mn></mfrac><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>11</mn><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mn>121</mn><mn>9</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Si (a+b)2 = a2+ 2ab + b2, el resultat es calcula doncs amb:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#0000FF¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨»x«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msup mathcolor=¨#0000FF¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mstyle»«/math»

]]> 1.2.0.214Q QuadratSumaGsup1Gsup1 Calcula (#m)2

]]> Es calcula amb (#a_1 x#n)2 + 2·(#a_1 x#n)·(#a_2 x#p) + (#a_2 x#p)2

]]> 1.0000000 0.5000000 0 0 #s_32 <question><wirisCasSession>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;apply&gt;&lt;csymbol definitionURL=&quot;http://www.wiris.com/XML/csymbol&quot;&gt;repeat&lt;/csymbol&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd/&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;&amp;gt;&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/apply&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_32&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_32&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;36&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;8&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;24&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml">#s_32</correctAnswer></correctAnswers><localData><data name="inputField">textField</data></localData></question> 1.2.0.215Q QuadratSuma xyGAleat Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»m«/mi»«msup mathcolor=¨#003300¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«/mstyle»«/math»


]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mrow><mn>2</mn><mo>,</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>aleatori</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>11</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>11</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced><mo>*</mo><msup><mi>y</mi><mi>e2</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>A</mi><mo>+</mo><mi>B</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msup><mi>m</mi><mn>2</mn></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>5</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>y</mi><mn>5</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>5</mn></msup><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>y</mi><mn>5</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>81</mn><mo>*</mo><msup><mi>x</mi><mn>10</mn></msup><mo>-</mo><mn>162</mn><mo>*</mo><msup><mi>x</mi><mn>5</mn></msup><mo>*</mo><msup><mi>y</mi><mn>5</mn></msup><mo>+</mo><mn>81</mn><mo>*</mo><msup><mi>y</mi><mn>10</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">8</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> (A + B)2 = A2 + 2·A·B + B2

 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#0000FF¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msup mathcolor=¨#0000FF¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»A«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»A«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»B«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msup mathcolor=¨#0000FF¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»B«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/math»

 

 

 

]]> 1.2.0.221Q QuadratDiferènciaG1G0 Calcula (#m)2

]]> Com que (#m) = (#a_1 x) + (#a_2)
es calcula amb (#a_1 x)2 + 2·(#a_1 x)·(#a_2) + (#a_2)2

]]> 1.0000000 0.5000000 0 0 #s_32 <question><wirisCasSession>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_32&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_32&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;16&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;16&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml">#s_32</correctAnswer></correctAnswers><localData><data name="inputField">textField</data></localData></question> 1.2.0.222Q QuadratDiferènciaG1G0_2 Calcula (#m)2

]]> Com que (#m) = (#a_1 x) + (#a_2)
es calcula amb (#a_1 x)2 + 2·(#a_1 x)·(#a_2) + (#a_2)2

]]> 1.0000000 0.5000000 0 0 #s_32 <question><wirisCasSession>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_32&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;8&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;8&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_32&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;32&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;64&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml">#s_32</correctAnswer></correctAnswers><localData><data name="inputField">textField</data></localData></question> 1.2.0.223Q QuadratDiferènciaGsup1G0 Calcula (#m)2

]]> Com que #m = (#a_1 x#n)+ (#a_2)
Es calcula amb (#a_1 x#n)2 + 2·(#a_1 x#n)·(#a_2) + (#a_2)2

]]> 1.0000000 0.5000000 0 0 #s_32 <question><wirisCasSession>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_32&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;10&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;10&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_32&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;121&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;12&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;220&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;100&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml">#s_32</correctAnswer></correctAnswers><localData><data name="inputField">textField</data></localData></question> 1.2.0.224Q QuadratDiferènciaGsup1Gsup1 Calcula (#m)2

]]> Com que #m = (#a_1 x#n) + (#a_2 x#p)
es calcula amb (#a_1 x#n)2 + 2·(#a_1 x#n)·(#a_2 x#p) + (#a_2 x#p)2

]]> 1.0000000 0.5000000 0 0 #s_32 <question><wirisCasSession>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;apply&gt;&lt;csymbol definitionURL=&quot;http://www.wiris.com/XML/csymbol&quot;&gt;repeat&lt;/csymbol&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd/&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;&amp;gt;&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/apply&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_32&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;10&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;10&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;10&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;10&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_32&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;100&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;12&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;200&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;10&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;100&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;8&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml">#s_32</correctAnswer></correctAnswers><localData><data name="inputField">textField</data></localData></question> 1.2.0.225Q QuadratDiferència Frac Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»m«/mi»«msup mathcolor=¨#003300¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«/mstyle»«/math»


]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>11</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>c_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>11</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_1</mi><mo>=</mo><mfrac><mi>b_1</mi><mi>c_1</mi></mfrac></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>b_1</mi><mo>&nbsp;</mo><mi>mod</mi><mo>&nbsp;</mo><mi>c_1</mi></mrow></mfenced><mo>&ne;</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>11</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>c_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>11</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mfrac><mi>b_2</mi><mi>c_2</mi></mfrac></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>b_1</mi><mo>&nbsp;</mo><mi>mod</mi><mo>&nbsp;</mo><mi>c_1</mi></mrow></mfenced><mo>&ne;</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>a_1</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>a_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>(</mo><mi>a_1</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>a_2</mi><msup><mo>)</mo><mn>2</mn></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mfrac><mn>3</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mfrac><mn>3</mn><mn>5</mn></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mn>9</mn><mn>25</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Si (a-b)2 = a2- 2ab + b2, el resultat es calcula doncs amb:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#0000FF¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨»x«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msup mathcolor=¨#0000FF¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mstyle»«/math»

]]> 1.2.0.30DT TREURE FACTOR COMÚ  

Treure factor comú

Per treure factor comú a una expressió algèbrica, cal calcular el mcd dels sumands.
Exemple:
18x5 - 9x4 + 36x3 - 27x2 = 9x2(2x3 - x2 + 4x - 3)
El quadrat d'un binomi i la diferència de quadrats poden ser útils.
Treure factor comú pot ajudar a simplificar:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»3«/mn»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»+«/mo»«mn»6«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»3«/mn»«mi»x«/mi»«/mrow»«mrow»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»2«/mn»«mi»x«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»3«/mn»«mi»x«/mi»«mfenced»«mrow»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»2«/mn»«mi»x«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»2«/mn»«mi»x«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mn»3«/mn»«mi»x«/mi»«mo»§#160;«/mo»«/math»



 
]]> 0.0000000 0.0000000 0 1.2.0.31Q Factoritzar quadrat suma Factoritza: #e 


]]> 1.0000000 0.5000000 0 0 #sol  

]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a2</mi><msup><mo>)</mo><mn>2</mn></msup><mo> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a2</mi><msup><mo>)</mo><mn>2</mn></msup><mo> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><msup><mfenced><mi>a2</mi></mfenced><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>e</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mn>17</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>34</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>289</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>34</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>289</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>34</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>289</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>17</mn></mrow></mfenced><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Es poden calcular les arrels de l'expressió de segon grau, resolent l'equació corresponent. 

Però també es pot identificar un quadrat perfecte,

si es treu #a1 en factor: #a1 · (#e1); 

s'identifica el doble producte 2·#a2 = #p

i el quadrat del segon (#a2)2 = #q

 

]]> 1.2.0.32Q Factoritzar quadrat diferència Factoritza: #e 


]]> 1.0000000 0.5000000 0 0 #sol  

]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a2</mi><msup><mo>)</mo><mn>2</mn></msup><mo> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a2</mi><msup><mo>)</mo><mn>2</mn></msup><mo> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><msup><mfenced><mi>a2</mi></mfenced><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>e</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>36</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>162</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>18</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>81</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>81</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mn>9</mn></mrow></mfenced><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Es poden calcular les arrels de l'expressió de segon grau, resolent l'equació corresponent. 

Però també es pot identificar un quadrat perfecte,

si es treu #a1 en factor: #a1 · (#e1); 

s'identifica el doble producte 2·#a2 = #p

i el quadrat del segon (#a2)2 = #q

 

]]> 1.2.0.33Q Factoritzar diferència quadrats Factoritza: #e 


]]> 1.0000000 0.5000000 0 0 #sol  

]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a2</mi><mo>)</mo><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mi>a2</mi></mrow></mfenced><mo> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a2</mi><mo>)</mo><mo> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><msup><mfenced><mi>a2</mi></mfenced><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>e</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>,</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>320</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>64</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>64</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>8</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>8</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Es poden calcular les arrels de l'expressió de segon grau, resolent l'equació corresponent. 

Però també es pot identificar una diferència de quadrats,

si es treu #a1 en factor: #a1 · (#e1); 

es veu que #q = #a22 

 

]]> 1.2.0.34Q Factoritzar P(x,y,z) Factoritza: #e 


]]> 1.0000000 0.5000000 0 0 #sol  

]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>p1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>p2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>p3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>p4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>p1</mi><mo>≠</mo><mi>p2</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>p1</mi><mo>≠</mo><mi>p3</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><msup><mfenced><mi>a1</mi></mfenced><mfenced><mi>q1</mi></mfenced></msup><mo>*</mo><mo>(</mo><mi>a2</mi><msup><mo>)</mo><mfenced><mi>q2</mi></mfenced></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><msup><mfenced><mi>a1</mi></mfenced><mfenced><mi>q2</mi></mfenced></msup><mo>*</mo><mo>(</mo><mi>a2</mi><msup><mo>)</mo><mfenced><mi>q3</mi></mfenced></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><msup><mfenced><mi>a1</mi></mfenced><mfenced><mi>q1</mi></mfenced></msup><mo>*</mo><mo>(</mo><mi>a2</mi><msup><mo>)</mo><mfenced><mi>q4</mi></mfenced></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><msup><mi>x</mi><mfenced><mi>p1</mi></mfenced></msup><mo>*</mo><msup><mi>y</mi><mfenced><mi>p2</mi></mfenced></msup><mo>*</mo><msup><mi>z</mi><mfenced><mi>p3</mi></mfenced></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><msup><mi>x</mi><mfenced><mi>p2</mi></mfenced></msup><mo>*</mo><msup><mi>y</mi><mfenced><mi>p3</mi></mfenced></msup><mo>*</mo><msup><mi>z</mi><mfenced><mi>p4</mi></mfenced></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><msup><mi>x</mi><mfenced><mi>p3</mi></mfenced></msup><mo>*</mo><msup><mi>y</mi><mfenced><mi>p4</mi></mfenced></msup><mo>*</mo><msup><mi>z</mi><mfenced><mi>p1</mi></mfenced></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>c1</mi><mo>*</mo><mi>t1</mi><mo>+</mo><mi>c2</mi><mo>*</mo><mi>t2</mi><mo>+</mo><mi>c3</mi><mo>*</mo><mi>t3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>e</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mi>mínim</mi><mo>(</mo><mi>p1</mi><mo>,</mo><mi>p2</mi><mo>,</mo><mi>p3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi><mo>=</mo><mi>mínim</mi><mo>(</mo><mi>p2</mi><mo>,</mo><mi>p3</mi><mo>,</mo><mi>p4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m3</mi><mo>=</mo><mi>mínim</mi><mo>(</mo><mi>p1</mi><mo>,</mo><mi>p3</mi><mo>,</mo><mi>p4</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>,</mo><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>*</mo><msup><mi>z</mi><mn>4</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup><mo>*</mo><msup><mi>z</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>4</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>*</mo><msup><mi>z</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>*</mo><msup><mi>z</mi><mn>3</mn></msup><mo>+</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>*</mo><msup><mi>z</mi><mn>4</mn></msup><mo>+</mo><mn>18</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup><mo>*</mo><msup><mi>z</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>,</mo><mi>m2</mi><mo>,</mo><mi>m3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>z</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><mi>y</mi><mo>+</mo><mi>x</mi><mo>*</mo><mi>z</mi><mo>+</mo><mn>3</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Per treure factor comú:

  • cal fer la descomposició en factors de #c1, #c2 i #c3 per trobar-ne el mcd. 
  • cal mirar quina és l'exponent més petit per cada una de les variables en els 3 sumands: per la x, #m1; per la y, #m2; i per la z, #m3.

 

]]> 1.2.0.50DT SigneExpressió1rGrau

Signe de ax + b
x -∞ -b/a +∞
ax+b Signe contrari de a 0 Signe de a




]]> 0.0000000 0.0000000 0 Resol: #e #v 0

Format de la resposta: x<-2/5 (SIMPLIFICADA)

]]> #e #v 0 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8660;«/mo»«/math» #sol

]]> 1.0000000 0.5000000 0 0 #sol  

]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>&gt;</mo><mo>&quot;</mo></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mo>-</mo><mi>b</mi><mo>/</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>v</mi><mo>=</mo><mo>&quot;</mo><mo>&gt;</mo><mo>&quot;</mo></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mi>x</mi><mo>&gt;</mo><mi>s</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mi>x</mi><mo>&lt;</mo><mi>s</mi></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>m_2</mi><mo>=</mo><mo>&quot;</mo><mi>positiva</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>n_2</mi><mo>=</mo><mo>&quot;</mo><mi>signe</mi><mo> </mo><mi>de</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>m_1</mi><mo>=</mo><mo>&quot;</mo><mi>negativa</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>n_1</mi><mo>=</mo><mo>&quot;</mo><mi>signe</mi><mo> </mo><mi>contrari</mi><mo> </mo><mi>de</mi><mo>&quot;</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_1</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_2</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>&lt;</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_81</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&lt;</mo><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>negativa</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>signe</ms><mo> </mo><ms>contrari</ms><mo> </mo><ms>de</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>positiva</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>signe</ms><mo> </mo><ms>de</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer cal resoldre:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»e«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8660;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8660;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8201;«/mo»«mfrac mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«/math»

Després cal fer la taula de signes.

 

]]> La taula de signes mostra que:

    • pels valors de x inferiors a #s, l'expressió és #m_1 (#n_1 #a)
    • pels valors de x superiors a #s, l'expressió és #m_2 (#n_2 #a)

 

x «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mo»§#8734;«/mo»«/math» #s
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»+«/mo»«mo»§#8734;«/mo»«/math»
#e #s_1 0 #s_2
]]> 1.2.0.52Q Resoldre ax+bSUP0 (a NEGATIU) Resol: #e #v  0

Format de la resposta: x<-2/5 (SIMPLIFICADA)

]]> #e #v 0 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8660;«/mo»«/math» #sol

]]> 1.0000000 0.5000000 0 0 #sol  

]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>&gt;</mo><mo>&quot;</mo></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mo>-</mo><mi>b</mi><mo>/</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>v</mi><mo>=</mo><mo>&quot;</mo><mo>&gt;</mo><mo>&quot;</mo></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mi>x</mi><mo>&lt;</mo><mi>s</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mi>x</mi><mo>&gt;</mo><mi>s</mi></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>m_2</mi><mo>=</mo><mo>&quot;</mo><mi>negativa</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>n_2</mi><mo>=</mo><mo>&quot;</mo><mi>signe</mi><mo> </mo><mi>de</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>m_1</mi><mo>=</mo><mo>&quot;</mo><mi>positiva</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>n_1</mi><mo>=</mo><mo>&quot;</mo><mi>signe</mi><mo> </mo><mi>contrari</mi><mo> </mo><mi>de</mi><mo>&quot;</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_1</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_2</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>&lt;</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_81</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&lt;</mo><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>negativa</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>signe</ms><mo> </mo><ms>contrari</ms><mo> </mo><ms>de</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>positiva</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>signe</ms><mo> </mo><ms>de</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer cal resoldre:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»e«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8660;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8660;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8201;«/mo»«mfrac mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«/math»

Després cal fer la taula de signes.

 

]]> La taula de signes mostra que:

    • pels valors de x inferiors a #s, l'expressió és #m_1 (#n_1 #a)
    • pels valors de x superiors a #s, l'expressió és #m_2 (#n_2 #a)

 

x «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mo»§#8734;«/mo»«/math» #s
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»+«/mo»«mo»§#8734;«/mo»«/math»
#e #s_1 0 #s_2
]]> 1.2.0.53Q Resoldre ax+b0 (a,b aleatoris) Resol: #e #v 0

Format de la resposta: x<-2/5 (SIMPLIFICADA)

]]> #e #v 0 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8660;«/mo»«/math» #sol

]]> 1.0000000 0.3333333 0 0 #sol  

]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>19</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>&gt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩽</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩾</mo><mo>&quot;</mo></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mo>-</mo><mi>b</mi><mo>/</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>v</mi><mo>=</mo><mo>&quot;</mo><mo>&gt;</mo><mo>&quot;</mo></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mi>x</mi><mo>&gt;</mo><mi>s</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>v</mi><mo>=</mo><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo></mrow><mrow><mi>sol</mi><mo>=</mo><mi>x</mi><mo>&lt;</mo><mi>s</mi></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>v</mi><mo>=</mo><mo>&quot;</mo><mo>⩽</mo><mo>&quot;</mo></mrow><mrow><mi>sol</mi><mo>=</mo><mi>x</mi><mo>⩽</mo><mi>s</mi></mrow><mrow><mi>sol</mi><mo>=</mo><mi>x</mi><mo>⩾</mo><mi>s</mi></mrow></apply></apply></mtd></mtr><mtr><mtd/></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>m_2</mi><mo>=</mo><mo>&quot;</mo><mi>positiva</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>n_2</mi><mo>=</mo><mo>&quot;</mo><mi>signe</mi><mo> </mo><mi>de</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>m_1</mi><mo>=</mo><mo>&quot;</mo><mi>negativa</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>n_1</mi><mo>=</mo><mo>&quot;</mo><mi>signe</mi><mo> </mo><mi>contrari</mi><mo> </mo><mi>de</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s_1</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s_2</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>v</mi><mo>=</mo><mo>&quot;</mo><mo>&gt;</mo><mo>&quot;</mo></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mi>x</mi><mo>&lt;</mo><mi>s</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>v</mi><mo>=</mo><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo></mrow><mrow><mi>sol</mi><mo>=</mo><mi>x</mi><mo>&gt;</mo><mi>s</mi></mrow><apply><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>⩾</mo><mfrac><mn>7</mn><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>positiva</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>signe</ms><mo> </mo><ms>de</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>negativa</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>signe</ms><mo> </mo><ms>contrari</ms><mo> </mo><ms>de</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer cal resoldre:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»e«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8660;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8660;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8201;«/mo»«mfrac mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«/math»

Després cal fer la taula de signes.

 

]]> La taula de signes mostra que:

    • pels valors de x inferiors a #s, l'expressió és #m_1 (#n_1 #a)
    • pels valors de x superiors a #s, l'expressió és #m_2 (#n_2 #a)

 

x «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mo»§#8734;«/mo»«/math» #s
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»+«/mo»«mo»§#8734;«/mo»«/math»
#e #s_1 0 #s_2
]]> 1.2.0.60DT SIGNEPOL G2 FACTORS

Signe de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«msup mathcolor=¨#FFFFC3¨»«mi mathcolor=¨#FFFFC3¨»ax«/mi»«mn»2«/mn»«/msup»«mo mathcolor=¨#FFFFC3¨»+«/mo»«mi mathcolor=¨#FFFFC3¨»bx«/mi»«mo mathcolor=¨#FFFFC3¨»+«/mo»«mi mathvariant=¨normal¨ mathcolor=¨#FFFFC3¨»c«/mi»«/mstyle»«/math»

Si no té solucions, té el signe de a.

Si té solució doble x1, té el signe de a excepte en x1

Si té dues solucions, x1< x2:

x -∞ x1   x2 +∞
a Signe de a 0 Signe de a 0 Signe de a
x-x1 —  0 +   +
x-x2 —   —  0 +
ax2+bx+c Signe de a   Contrari de a   Signe de a




]]> 0.0000000 0.0000000 0 1.2.0.61Q Resol ax^2+bx+c factoritzant Factoritza i resol: #e #v 0

Format de la resposta:

Factoritza: 2(x-1)(x-2)

Resol:

  • Entre dos nombres:  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mn»2«/mn»«mo»§lt;«/mo»«mi»x«/mi»«mo»§#8743;«/mo»«mn»5«/mn»«mo»§lt;«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#8743;«/mo»«mo»=«/mo»«mi»i«/mi»«mo»)«/mo»«/math»
  • Altres situacions:  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§lt;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#8744;«/mo»«mi»x«/mi»«mo»§#62;«/mo»«mn»5«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#8744;«/mo»«mo»=«/mo»«mi»o«/mi»«mo»)«/mo»«/math»
]]> 1.0000000 0.3333333 0 0 Factoritza=#f5Resol =#sol]]>  

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mathvariant="normal">e</mi><mi>s</mi><mi>o</mi><mi>l</mi><mo>&#160;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Primer es resol l'equació de 2n grau.

el discriminant és #d i les solucions són #x_1 i #x_2.

ES COMPROVEN AMB S = #S1 I P = #P1

Es pot factoritzar amb a·(x – x1)(x  – x2). No oblidis el signe de a

Després es fa la taula.

]]> La taula és:



Com que a és #r1,

#e és #r2, #r4, per x<#x_1  o  per x>#x_2

#e és #r3, #r5,  per #x_1<x   i   per x<#x_2
x –∞         #x_1             #x_2        +∞
a #s3   #s3   #s3
#k11 —  0 +    + 
#k12  —   —   0 + 
#e #s1 0 #s2 0 #s1




]]> 1.2.0.62Q Resol ax^2+bx+c factoritzant_2 Factoritza i resol:#e #v 0

Format de la resposta:

Factoritza: 2(x-1)(x-2)

Resol:

  • Entre dos nombres:  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mn»2«/mn»«mo»§lt;«/mo»«mi»x«/mi»«mo»§#8743;«/mo»«mn»5«/mn»«mo»§lt;«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#8743;«/mo»«mo»=«/mo»«mi»i«/mi»«mo»)«/mo»«/math»
  • Altres situacions:  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§lt;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#8744;«/mo»«mi»x«/mi»«mo»§#62;«/mo»«mn»5«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#8744;«/mo»«mo»=«/mo»«mi»o«/mi»«mo»)«/mo»«/math»
]]> 1.0000000 0.3333333 0 0 Factoritza=#f5Resol =#sol]]>  

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align="center"><mtr><mtd><mi>x</mi><mo>&gt;</mo><mn>2</mn><mo>,</mo><mi>x</mi><mo>&lt;</mo><mo>-</mo><mn>4</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>&lt;</mo><mo>-</mo><mn>4</mn><mo>,</mo><mi>x</mi><mo>&gt;</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>2</mn><mo>∨</mo><mi>x</mi><mo>&lt;</mo><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S1</mi><mo>,</mo><mi>P1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mi>a</mi><mi>c</mi><mi>t</mi><mi>o</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi>z</mi><mi>a</mi><mo>=</mo><mo>#</mo><mi>f</mi><mn>5</mn><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>o</mi><mi>l</mi><mo>&#160;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Primer es resol l'equació de 2n grau.

el discriminant és #d i les solucions són #x_1 i #x_2.

ES COMPROVEN AMB S = #S1 I P = #P1

Es pot factoritzar amb a·(x – x1)(x  – x2). No et deixis a

Després es fa la taula.

]]> Si fem la taula: 



Com que a és #r1,

#e és #r2, #r4, per x<#x_1  o  per x>#x_2

#e és #r3, #r5,  per #x_1<x   i   per x<#x_2
x –∞         #x_1             #x_2        +∞
a #s3   #s3   #s3
#k11 —  0 +    + 
#k12  —   —   0 + 
#e #s1 0 #s2 0 #s1




]]> 1.2.0.70DT SIGNEPOL G2 TAULA

Signe de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«msup mathcolor=¨#FFFFC3¨»«mi mathcolor=¨#FFFFC3¨»ax«/mi»«mn»2«/mn»«/msup»«mo mathcolor=¨#FFFFC3¨»+«/mo»«mi mathcolor=¨#FFFFC3¨»bx«/mi»«mo mathcolor=¨#FFFFC3¨»+«/mo»«mi mathvariant=¨normal¨ mathcolor=¨#FFFFC3¨»c«/mi»«/mrow»«/mstyle»«/math»
Si no té solució, té el signe de a.
Si té solució doble, té el signe de a excepte en x1.
Si té dues solucions, x1 i x2:
x -∞ x1   x2 +∞
ax2+bx+c Signe de a 0 Contrari de a 0 Signe de a




]]> 0.0000000 0.0000000 0 1.2.0.71Q Resol ax^2+bx+c Negatiu Resol: #e < 0

Format de la resposta:

Entre dos nombres: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«mo»§lt;«/mo»«mi»x«/mi»«mo»§#8743;«/mo»«mi»x«/mi»«mo»§lt;«/mo»«mn»5«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#8743;«/mo»«mo»=«/mo»«mi»i«/mi»«mo»)«/mo»«/math»

Altra situació: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§lt;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#8744;«/mo»«mi»x«/mi»«mo»§#62;«/mo»«mn»5«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#8744;«/mo»«mo»=«/mo»«mi»o«/mi»«mo»)«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol  

]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>x_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mfenced><mrow><mi>a</mi><mo>*</mo><mfenced><mrow><mi>x_1</mi><mo>+</mo><mi>x_2</mi></mrow></mfenced></mrow></mfenced><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>a</mi><mn>2</mn></msup><mo>*</mo><mi>x_1</mi><mo>*</mo><mi>x_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>e</mi><mo>&lt;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>resol_inequació</mi><mo>(</mo><mi>e1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi><mo>=</mo><msub><mi>R</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_2</mi><mo>=</mo><msub><mi>R</mi><mn>2</mn></msub></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>R</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S1</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mi>x_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi><mo>=</mo><mi>x_1</mi><mo>*</mo><mi>x_2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>x_1</mi><mo>,</mo><mi>x_2</mi><mo>,</mo><mi>d</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>400</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>r1</mi><mo>,</mo><mi>r2</mi><mo>,</mo><mi>r3</mi><mo>,</mo><mi>s1</mi><mo>,</mo><mi>s2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>positiu</ms><mo>,</mo><ms>positiu</ms><mo>,</mo><ms>negatiu</ms><mo>,</mo><mo>+</mo><mo>,</mo><mo>-</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>48</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mo>-</mo><mn>6</mn><mo>∧</mo><mi>x</mi><mo>&lt;</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&lt;</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>&gt;</mo><mo>-</mo><mn>6</mn><mo>,</mo><mi>x</mi><mo>&lt;</mo><mn>4</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>&lt;</mo><mn>4</mn><mo>,</mo><mi>x</mi><mo>&gt;</mo><mo>-</mo><mn>6</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mo>-</mo><mn>6</mn><mo>∧</mo><mi>x</mi><mo>&lt;</mo><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer es resol l'equació de 2n grau.

el discriminant és #d i les solucions són #x_1 i #x_2.

(ES COMPROVEN AMB S = #S1  I P = #P1)

Després faig la taula.

]]> La taula és:


Com que a és #r1,
x -∞ #x_1   #x_2 +∞
#e #s1 0 #s2 0 #s1




]]> 1.2.0.72Q Resol ax^2+bx+c Positiu Resol: #e > 0

Format de la resposta:

Entre dos nombres: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«mo»§lt;«/mo»«mi»x«/mi»«mo»§#8743;«/mo»«mi»x«/mi»«mo»§lt;«/mo»«mn»5«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#8743;«/mo»«mo»=«/mo»«mi»i«/mi»«mo»)«/mo»«/math»

Altra situació: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§lt;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#8744;«/mo»«mi»x«/mi»«mo»§#62;«/mo»«mn»5«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#8744;«/mo»«mo»=«/mo»«mi»o«/mi»«mo»)«/mo»«/math»

]]> #e > 0  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8660;«/mo»«/math» #sol

]]> 1.0000000 0.3333333 0 0 #sol  

]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>x_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>x_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>x_1</mi><mo>&lt;</mo><mi>x_2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x_1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x_2</mi><mo>)</mo><mo> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mfenced><mrow><mi>a</mi><mo>*</mo><mfenced><mrow><mi>x_1</mi><mo>+</mo><mi>x_2</mi></mrow></mfenced></mrow></mfenced><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>a</mi><mn>2</mn></msup><mo>*</mo><mi>x_1</mi><mo>*</mo><mi>x_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>e</mi><mo>&gt;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>resol_inequació</mi><mo>(</mo><mi>e1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi><mo>=</mo><msub><mi>R</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_2</mi><mo>=</mo><msub><mi>R</mi><mn>2</mn></msub></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><ms>positiu</ms><mo>,</mo><ms>positiu</ms><mo>,</mo><ms>negatiu</ms><mo>,</mo><mo>+</mo><mo>,</mo><mo>-</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>48</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mo>-</mo><mn>6</mn><mo>∧</mo><mi>x</mi><mo>&lt;</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&lt;</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>&gt;</mo><mo>-</mo><mn>6</mn><mo>,</mo><mi>x</mi><mo>&lt;</mo><mn>4</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>&lt;</mo><mn>4</mn><mo>,</mo><mi>x</mi><mo>&gt;</mo><mo>-</mo><mn>6</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mo>-</mo><mn>6</mn><mo>∧</mo><mi>x</mi><mo>&lt;</mo><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer es resol l'equació de 2n grau.

el discriminant és #d i les solucions són #x_1 i #x_2.

(ES COMPROVEN AMB S = #S1  I P = #P1)

Després es fa la taula.

]]> La taula és:



Com que a és #r1,

#e és #r2 (signe de a), #r4, per x<#x_1   o   per x>#x_2

#e és #r3 (signe contrari de a), #r5,  per #x_1<x   i   per x<#x_2
x -∞ #x_1   #x_2 +∞
#e #s1 0 #s2 0 #s1




]]> 1.2.0.73Q Resol ax^2+bx+c ALEATORI Resol: #e #v 0

Format de la resposta:

Entre dos nombres:  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mn»2«/mn»«mo»§lt;«/mo»«mi»x«/mi»«mo»§#8743;«/mo»«mn»5«/mn»«mo»§lt;«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#8743;«/mo»«mo»=«/mo»«mi»i«/mi»«mo»)«/mo»«/math»

Altres situacions:  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§lt;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#8744;«/mo»«mi»x«/mi»«mo»§#62;«/mo»«mn»5«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#8744;«/mo»«mo»=«/mo»«mi»o«/mi»«mo»)«/mo»«/math»

]]>  

]]> 1.0000000 0.3333333 0 0 #sol  

]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>x_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>resol_inequació</mi><mo>(</mo><mi>e1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi><mo>=</mo><msub><mi>R</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_2</mi><mo>=</mo><msub><mi>R</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi><mo>=</mo><mo>{</mo><mi>t_1</mi><mo>,</mo><mi>t_2</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi><mo>=</mo><mo>{</mo><mi>t_2</mi><mo>,</mo><mi>t_1</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>R</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S1</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mi>x_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi><mo>=</mo><mi>x_1</mi><mo>*</mo><mi>x_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>x_1</mi><mo>,</mo><mi>x_2</mi><mo>,</mo><mi>d</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>81</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>r1</mi><mo>,</mo><mi>r2</mi><mo>,</mo><mi>r3</mi><mo>,</mo><mi>s1</mi><mo>,</mo><mi>s2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>negatiu</ms><mo>,</mo><ms>negatiu</ms><mo>,</mo><ms>positiu</ms><mo>,</mo><mo>-</mo><mo>,</mo><mo>+</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>45</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>162</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>9</mn><mo>∨</mo><mi>x</mi><mo>&lt;</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&lt;</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>&gt;</mo><mn>9</mn><mo>,</mo><mi>x</mi><mo>&lt;</mo><mn>6</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>&lt;</mo><mn>6</mn><mo>,</mo><mi>x</mi><mo>&gt;</mo><mn>9</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>9</mn><mo>∨</mo><mi>x</mi><mo>&lt;</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S1</mi><mo>,</mo><mi>P1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>,</mo><mn>54</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer es resol l'equació de 2n grau.

el discriminant és #d i les solucions són #x_1 i #x_2.

ES COMPROVEN AMB S = #S1 I P = #P1

Després es fa la taula.

]]> La taula: 



Com que a és #r1,

#e és #r2 (signe de a), #r4, per x<#x_1  o  per x>#x_2

#e és #r3 (signe contrari de a), #r5,  per #x_1<x   i   per x<#x_2
x -∞ #x_1   #x_2 +∞
#e #s1 0 #s2 0 #s1




]]> 1.2.0.74Q Resol ax^2+bx+c ALEATORI_2 Resol: #e #v 0

Format de la resposta:

Entre dos nombres:  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mn»2«/mn»«mo»§lt;«/mo»«mi»x«/mi»«mo»§#8743;«/mo»«mn»5«/mn»«mo»§lt;«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#8743;«/mo»«mo»=«/mo»«mi»i«/mi»«mo»)«/mo»«/math»

Altres situacions:  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§lt;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#8744;«/mo»«mi»x«/mi»«mo»§#62;«/mo»«mn»5«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#8744;«/mo»«mo»=«/mo»«mi»o«/mi»«mo»)«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol  

]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>x_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>x_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>x_1</mi><mo>&lt;</mo><mi>x_2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x_1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x_2</mi><mo>)</mo><mo> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mfenced><mrow><mi>a</mi><mo>*</mo><mfenced><mrow><mi>x_1</mi><mo>+</mo><mi>x_2</mi></mrow></mfenced></mrow></mfenced><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>a</mi><mn>2</mn></msup><mo>*</mo><mi>x_1</mi><mo>*</mo><mi>x_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>&gt;</mo><mo>&quot;</mo></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>v</mi><mo>=</mo><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo></mrow><mtable><mtr><mtd><mi>e1</mi><mo>=</mo><mi>e</mi><mo>&lt;</mo><mn>0</mn></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>r1</mi><mo>=</mo><mo>&quot;</mo><mi>positiu</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mo>&quot;</mo><mi>positiu</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mo>&quot;</mo><mi>negatiu</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r4</mi><mo>=</mo><mo>&quot;</mo><mo> </mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r5</mi><mo>=</mo><mo>&quot;</mo><mi>i</mi><mo> </mo><mi>és</mi><mo> </mo><mi>el</mi><mo> </mo><mi>que</mi><mo> </mo><mi>demana</mi><mo> </mo><mi>l</mi><mo>&apos;</mo><mi>enunciat</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><mi>r1</mi><mo>=</mo><mo>&quot;</mo><mi>negatiu</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mo>&quot;</mo><mi>negatiu</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mo>&quot;</mo><mi>positiu</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r5</mi><mo>=</mo><mo>&quot;</mo><mo> </mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r4</mi><mo>=</mo><mo>&quot;</mo><mi>i</mi><mo> </mo><mi>és</mi><mo> </mo><mi>el</mi><mo> </mo><mi>que</mi><mo> </mo><mi>demana</mi><mo> </mo><mi>l</mi><mo>&apos;</mo><mi>enunciat</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable></apply></mtd></mtr></mtable><mtable><mtr><mtd><mi>e1</mi><mo>=</mo><mi>e</mi><mo>&gt;</mo><mn>0</mn></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>r1</mi><mo>=</mo><mo>&quot;</mo><mi>positiu</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mo>&quot;</mo><mi>positiu</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mo>&quot;</mo><mi>negatiu</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r5</mi><mo>=</mo><mo>&quot;</mo><mo> </mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r4</mi><mo>=</mo><mo>&quot;</mo><mi>i</mi><mo> </mo><mi>és</mi><mo> </mo><mi>el</mi><mo> </mo><mi>que</mi><mo> </mo><mi>demana</mi><mo> </mo><mi>l</mi><mo>&apos;</mo><mi>enunciat</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><mi>r1</mi><mo>=</mo><mo>&quot;</mo><mi>negatiu</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mo>&quot;</mo><mi>negatiu</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mo>&quot;</mo><mi>positiu</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r4</mi><mo>=</mo><mo>&quot;</mo><mo> </mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r5</mi><mo>=</mo><mo>&quot;</mo><mi>i</mi><mo> </mo><mi>és</mi><mo> </mo><mi>el</mi><mo> </mo><mi>que</mi><mo> </mo><mi>demana</mi><mo> </mo><mi>l</mi><mo>&apos;</mo><mi>enunciat</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable></apply></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>resol_inequació</mi><mo>(</mo><mi>e1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi><mo>=</mo><msub><mi>R</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_2</mi><mo>=</mo><msub><mi>R</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi><mo>=</mo><mo>{</mo><mi>t_1</mi><mo>,</mo><mi>t_2</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi><mo>=</mo><mo>{</mo><mi>t_2</mi><mo>,</mo><mi>t_1</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>R</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S1</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mi>x_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi><mo>=</mo><mi>x_1</mi><mo>*</mo><mi>x_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>x_1</mi><mo>,</mo><mi>x_2</mi><mo>,</mo><mi>d</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>81</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>r1</mi><mo>,</mo><mi>r2</mi><mo>,</mo><mi>r3</mi><mo>,</mo><mi>s1</mi><mo>,</mo><mi>s2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>negatiu</ms><mo>,</mo><ms>negatiu</ms><mo>,</mo><ms>positiu</ms><mo>,</mo><mo>-</mo><mo>,</mo><mo>+</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>45</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>162</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>9</mn><mo>∨</mo><mi>x</mi><mo>&lt;</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&lt;</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>&gt;</mo><mn>9</mn><mo>,</mo><mi>x</mi><mo>&lt;</mo><mn>6</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>&lt;</mo><mn>6</mn><mo>,</mo><mi>x</mi><mo>&gt;</mo><mn>9</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>9</mn><mo>∨</mo><mi>x</mi><mo>&lt;</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S1</mi><mo>,</mo><mi>P1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>,</mo><mn>54</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer es resol l'equació de 2n grau.

el discriminant és #d i les solucions són #x_1 i #x_2.

ES COMPROVEN AMB S = #S1 I P = #P1

Després es fa la taula.

]]> La taula: 



Com que a és #r1,

#e és #r2 (signe de a), #r4, per x<#x_1  o  per x>#x_2

#e és #r3 (signe contrari de a), #r5,  per #x_1<x   i   per x<#x_2
x -∞ #x_1   #x_2 +∞
#e #s1 0 #s2 0 #s1




]]> 1.2.0.75Q Resol ax^2+bx+c ALEATORI_3 Resol: #e #v 0

Format de la resposta:

Entre dos nombres:  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mn»2«/mn»«mo»§lt;«/mo»«mi»x«/mi»«mo»§#8743;«/mo»«mn»5«/mn»«mo»§lt;«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#8743;«/mo»«mo»=«/mo»«mi»i«/mi»«mo»)«/mo»«/math»

Altres situacions:  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§lt;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#8744;«/mo»«mi»x«/mi»«mo»§#62;«/mo»«mn»5«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#8744;«/mo»«mo»=«/mo»«mi»o«/mi»«mo»)«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol  

]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>x_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>x_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>x_1</mi><mo>&lt;</mo><mi>x_2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x_1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x_2</mi><mo>)</mo><mo> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mfenced><mrow><mi>a</mi><mo>*</mo><mfenced><mrow><mi>x_1</mi><mo>+</mo><mi>x_2</mi></mrow></mfenced></mrow></mfenced><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>a</mi><mn>2</mn></msup><mo>*</mo><mi>x_1</mi><mo>*</mo><mi>x_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>&gt;</mo><mo>&quot;</mo></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>v</mi><mo>=</mo><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo></mrow><mtable><mtr><mtd><mi>e1</mi><mo>=</mo><mi>e</mi><mo>&lt;</mo><mn>0</mn></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>r1</mi><mo>=</mo><mo>&quot;</mo><mi>positiu</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mo>&quot;</mo><mi>positiu</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mo>&quot;</mo><mi>negatiu</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r4</mi><mo>=</mo><mo>&quot;</mo><mo> </mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r5</mi><mo>=</mo><mo>&quot;</mo><mi>i</mi><mo> </mo><mi>és</mi><mo> </mo><mi>el</mi><mo> </mo><mi>que</mi><mo> </mo><mi>demana</mi><mo> </mo><mi>l</mi><mo>&apos;</mo><mi>enunciat</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><mi>r1</mi><mo>=</mo><mo>&quot;</mo><mi>negatiu</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mo>&quot;</mo><mi>negatiu</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mo>&quot;</mo><mi>positiu</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r5</mi><mo>=</mo><mo>&quot;</mo><mo> </mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r4</mi><mo>=</mo><mo>&quot;</mo><mi>i</mi><mo> </mo><mi>és</mi><mo> </mo><mi>el</mi><mo> </mo><mi>que</mi><mo> </mo><mi>demana</mi><mo> </mo><mi>l</mi><mo>&apos;</mo><mi>enunciat</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable></apply></mtd></mtr></mtable><mtable><mtr><mtd><mi>e1</mi><mo>=</mo><mi>e</mi><mo>&gt;</mo><mn>0</mn></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>r1</mi><mo>=</mo><mo>&quot;</mo><mi>positiu</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mo>&quot;</mo><mi>positiu</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mo>&quot;</mo><mi>negatiu</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r5</mi><mo>=</mo><mo>&quot;</mo><mo> </mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r4</mi><mo>=</mo><mo>&quot;</mo><mi>i</mi><mo> </mo><mi>és</mi><mo> </mo><mi>el</mi><mo> </mo><mi>que</mi><mo> </mo><mi>demana</mi><mo> </mo><mi>l</mi><mo>&apos;</mo><mi>enunciat</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><mi>r1</mi><mo>=</mo><mo>&quot;</mo><mi>negatiu</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mo>&quot;</mo><mi>negatiu</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mo>&quot;</mo><mi>positiu</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r4</mi><mo>=</mo><mo>&quot;</mo><mo> </mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r5</mi><mo>=</mo><mo>&quot;</mo><mi>i</mi><mo> </mo><mi>és</mi><mo> </mo><mi>el</mi><mo> </mo><mi>que</mi><mo> </mo><mi>demana</mi><mo> </mo><mi>l</mi><mo>&apos;</mo><mi>enunciat</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable></apply></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>resol_inequació</mi><mo>(</mo><mi>e1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi><mo>=</mo><msub><mi>R</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_2</mi><mo>=</mo><msub><mi>R</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi><mo>=</mo><mo>{</mo><mi>t_1</mi><mo>,</mo><mi>t_2</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi><mo>=</mo><mo>{</mo><mi>t_2</mi><mo>,</mo><mi>t_1</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>R</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S1</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mi>x_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi><mo>=</mo><mi>x_1</mi><mo>*</mo><mi>x_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>x_1</mi><mo>,</mo><mi>x_2</mi><mo>,</mo><mi>d</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>81</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>r1</mi><mo>,</mo><mi>r2</mi><mo>,</mo><mi>r3</mi><mo>,</mo><mi>s1</mi><mo>,</mo><mi>s2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>negatiu</ms><mo>,</mo><ms>negatiu</ms><mo>,</mo><ms>positiu</ms><mo>,</mo><mo>-</mo><mo>,</mo><mo>+</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>45</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>162</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>9</mn><mo>∨</mo><mi>x</mi><mo>&lt;</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&lt;</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>&gt;</mo><mn>9</mn><mo>,</mo><mi>x</mi><mo>&lt;</mo><mn>6</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>&lt;</mo><mn>6</mn><mo>,</mo><mi>x</mi><mo>&gt;</mo><mn>9</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>9</mn><mo>∨</mo><mi>x</mi><mo>&lt;</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S1</mi><mo>,</mo><mi>P1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>,</mo><mn>54</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer es resol l'equació de 2n grau.

el discriminant és #d i les solucions són #x_1 i #x_2.

ES COMPROVEN AMB S = #S1 I P = #P1

Després es fa la taula.

]]> La taula: 



Com que a és #r1,

#e és #r2 (signe de a), #r4, per x<#x_1  o  per x>#x_2

#e és #r3 (signe contrari de a), #r5,  per #x_1<x   i   per x<#x_2
x -∞ #x_1   #x_2 +∞
#e #s1 0 #s2 0 #s1




]]> 1.2.0.80DT SIGNE D'UNA FRACCIÓ
 
Signe d'una fracció
Recorda que:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨18px¨»«mrow»«mfrac mathcolor=¨#003300¨»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»+«/mo»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»-«/mo»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mfrac mathcolor=¨#003300¨»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»-«/mo»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»+«/mo»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«/mrow»«/mstyle»«/math»
]]> 0.0000000 0.0000000 0 1.2.0.81Q SigneFracció ax+b/x+c Aleat_1 Resol: #e #v 0

Format de la resposta:

Entre dos nombres: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«mo»§lt;«/mo»«mi»x«/mi»«mo»§#8743;«/mo»«mi»x«/mi»«mo»§lt;«/mo»«mn»5«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#8743;«/mo»«mo»=«/mo»«mi»i«/mi»«mo»)«/mo»«/math»  

Altra situació: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§lt;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#8744;«/mo»«mi»x«/mi»«mo»§#62;«/mo»«mn»3«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#8744;«/mo»«mo»=«/mo»«mi»o«/mi»«mo»)«/mo»«/math»

]]> Els intervals solució queden definits per #sol

]]> 1.0000000 0.5000000 0 0 #sol  

]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>x_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>x_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>x_1</mi><mo>&lt;</mo><mi>x_2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>&gt;</mo><mo>&quot;</mo></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x_1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>x_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x_1</mi><mo>)</mo></mrow><mrow><mi>x</mi><mo>-</mo><mi>x_2</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi><mo>=</mo><mi>e</mi><mo>&lt;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_2</mi><mo>=</mo><mi>e</mi><mo>&gt;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable 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definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>m_2</mi><mo>=</mo><mo>&quot;</mo><mi>negativa</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>n_2</mi><mo>=</mo><mo>&quot;</mo><mi>signe</mi><mo> </mo><mi>contrari</mi><mo> </mo><mi>de</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>m_1</mi><mo>=</mo><mo>&quot;</mo><mi>positiva</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>n_1</mi><mo>=</mo><mo>&quot;</mo><mi>signe</mi><mo> </mo><mi>de</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>d3</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>d4</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>d5</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s_1</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s_2</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><mi>m_2</mi><mo>=</mo><mo>&quot;</mo><mi>positiva</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>n_2</mi><mo>=</mo><mo>&quot;</mo><mi>signe</mi><mo> </mo><mi>contrari</mi><mo> </mo><mi>de</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>m_1</mi><mo>=</mo><mo>&quot;</mo><mi>negativa</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>n_1</mi><mo>=</mo><mo>&quot;</mo><mi>signe</mi><mo> </mo><mo> </mo><mi>de</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>d3</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>d4</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>d5</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s_1</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s_2</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>resol_inequació</mi><mfenced><mi>e_3</mi></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>x_1</mi><mo>,</mo><mi>x_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfrac><mo>&lt;</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>2</mn><mo>∧</mo><mi>x</mi><mo>&lt;</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&lt;</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi></math></input><output><math 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xmlns="http://www.w3.org/1998/Math/MathML"><ms>signe</ms><mo> </mo><ms>de</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>negativa</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>signe</ms><mo> </mo><ms>contrari</ms><mo> </mo><ms>de</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sig</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>positiva</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>2</mn><mo>∧</mo><mi>x</mi><mo>&lt;</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="equivalent_equations"/><assertion name="syntax_expression"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Cal fer la taula de signes per veure que:

  • pels valors de x inferiors a #x_1, l'expressió és #m_1 (#n_1 #a)
  • pels valors de x entre #x_1 i #x_2, l'expressió és #m_2 (#n_2 #a)
  • pels valors de x superiors a #x_2, l'expressió és #m_1 (#n_1 #a)
 
x -∞ #x_1   #x_2 +∞
#n #d3   0 #d4     #d5
#d #d6   #d7 0 #d8
#e #s_1 0 #s_2   #s_1

 

i l'enunciat demana que l'expressió sigui #sig

]]> 1.2.0.82Q SigneFracció ax+b/x+c Aleat_2 Resol: #e #v 0

Format de la resposta:

Entre dos nombres: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«mo»§lt;«/mo»«mi»x«/mi»«mo»§#8743;«/mo»«mi»x«/mi»«mo»§lt;«/mo»«mn»5«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#8743;«/mo»«mo»=«/mo»«mi»i«/mi»«mo»)«/mo»«/math»  

Altra situació: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§lt;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#8744;«/mo»«mi»x«/mi»«mo»§#62;«/mo»«mn»3«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#8744;«/mo»«mo»=«/mo»«mi»o«/mi»«mo»)«/mo»«/math»

]]> Els intervals solució queden definits per #sol

]]> 1.0000000 0.5000000 0 0 #sol  

]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>x_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>x_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>x_1</mi><mo>&lt;</mo><mi>x_2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>&gt;</mo><mo>&quot;</mo></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math 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align="center"><mtr><mtd><mi>e_1</mi><mo>,</mo><mi>e_2</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>resol_inequació</mi><mo>(</mo><mi>e_3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi><mo>=</mo><msub><mi>R</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_2</mi><mo>=</mo><msub><mi>R</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi><mo>=</mo><mo>{</mo><mi>t_1</mi><mo>,</mo><mi>t_2</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi><mo>=</mo><mo>{</mo><mi>t_2</mi><mo>,</mo><mi>t_1</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>d6</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d7</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d8</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>v</mi><mo>=</mo><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo></mrow><mrow><mi>sig</mi><mo>=</mo><mo>&quot;</mo><mi>negativa</mi><mo>&quot;</mo></mrow><mrow><mi>sig</mi><mo>=</mo><mo>&quot;</mo><mi>positiva</mi><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>resol_inequació</mi><mfenced><mi>e_3</mi></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>x_1</mi><mo>,</mo><mi>x_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfrac><mo>&lt;</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>2</mn><mo>∧</mo><mi>x</mi><mo>&lt;</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&lt;</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>&gt;</mo><mn>2</mn><mo>,</mo><mi>x</mi><mo>&lt;</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>&lt;</mo><mn>3</mn><mo>,</mo><mi>x</mi><mo>&gt;</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>positiva</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>signe</ms><mo> </mo><ms>de</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>negativa</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>signe</ms><mo> </mo><ms>contrari</ms><mo> </mo><ms>de</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sig</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>positiva</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>2</mn><mo>∧</mo><mi>x</mi><mo>&lt;</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="equivalent_equations"/><assertion name="syntax_expression"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Cal fer la taula de signes per veure que:

  • pels valors de x inferiors a #x_1, l'expressió és #m_1 (#n_1 #a)
  • pels valors de x entre #x_1 i #x_2, l'expressió és #m_2 (#n_2 #a)
  • pels valors de x superiors a #x_2, l'expressió és #m_1 (#n_1 #a)
 
x -∞ #x_1   #x_2 +∞
#n #d3   0 #d4     #d5
#d #d6   #d7 0 #d8
#e #s_1 0 #s_2   #s_1

 

i l'enunciat demana que l'expressió sigui #sig

]]> 1rBTX 02. POLINOMIS/1.2.1 Operar polinomis 1.2.1.10DT SUMA POLINOMIS  

Addició de polinomis
Per sumar polinomis, sumem els monomis de mateix grau.

Exemple:
(-2x4 + 7x3+ 6x2 + 3x - 1) + (4x3- 6x2 + 9x - 5) = -2x4 + 11x3 + 12x - 6
Perquè:
-2x4 + 0 = -2x4
7x3 + 4x3 = 11x3
6x2+ (- 6x2) = 0x2(que no s'escriu)
3x + 9x = 12x
- 1+(-5) = -6



]]> 0.0000000 0.0000000 0 1.2.1.11Q SumaG3G3 Amb els polinomis
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«/mrow»«/mstyle»«/math»
i «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«/mrow»«/mstyle»«/math»
Suma  P(x) + Q(x)

Format: 3x5+2x4-3x3+7x2-5x+9

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>a2</mi><mo>∨</mo><mi>b2</mi><mo>≠</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a3</mi><mo>*</mo><mi>b3</mi><mo>≠</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a4</mi><mo>∨</mo><mi>b4</mi><mo>≠</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a5</mi><mo>*</mo><mi>b5</mi><mo>≠</mo><mn>0</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>a2</mi><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mi>a3</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>a4</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>b2</mi><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mi>b3</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b4</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>9</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>11</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> N'hi ha prou amb sumar entre ells els monomis de mateix grau (sumem els coeficients i el grau es manté):

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»+«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»+«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»+«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»b«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»5«/mn»«mo mathvariant=¨bold¨»+«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»5«/mn»«/mrow»«/mfenced»«/mrow»«/mfenced»«/mstyle»«/math»

]]> 1.2.1.12Q SumaG4G4 Amb els polinomis
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«/mrow»«/mstyle»«/math»
i «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«/mrow»«/mstyle»«/math»
Suma  P(x) + Q(x)

Format: 3x5+2x4-3x3+7x2-5x+9

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>a1</mi><mo>∨</mo><mi>b1</mi><mo>≠</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a2</mi><mo>*</mo><mi>b2</mi><mo>≠</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a4</mi><mo>∨</mo><mi>b4</mi><mo>≠</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a5</mi><mo>*</mo><mi>b5</mi><mo>≠</mo><mn>0</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>a1</mi><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mi>a2</mi><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mi>a3</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>a4</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>b1</mi><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mi>b2</mi><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mi>b3</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b4</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> N'hi ha prou amb sumar entre ells els monomis de mateix grau (sumem els coeficients i el grau es manté):

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»+«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨»4«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»+«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»+«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»+«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»b«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»5«/mn»«mo mathvariant=¨bold¨»+«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»5«/mn»«/mrow»«/mfenced»«/mrow»«/mfenced»«/mstyle»«/math»

]]> 1.2.1.15Q SumaCoefFraccionaris Amb els polinomis
P(x) = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«/mrow»«/mstyle»«/math»
i Q(x) = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«/mrow»«/mstyle»«/math»
Calcula P(x) + Q(x)


]]>  

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a11</mi><mo>=</mo><mfrac><mi>a1</mi><mi>c1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a12</mi><mo>=</mo><mfrac><mi>a2</mi><mi>c2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a13</mi><mo>=</mo><mfrac><mi>a3</mi><mi>c1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a14</mi><mo>=</mo><mi>a4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a15</mi><mo>=</mo><mfrac><mi>a5</mi><mi>c2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mi>a1</mi><mi>c1</mi></mfrac><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mfrac><mi>a2</mi><mi>c2</mi></mfrac><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mfrac><mi>a3</mi><mi>c1</mi></mfrac><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>a4</mi><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mi>a5</mi><mi>c2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b11</mi><mo>=</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b12</mi><mo>=</mo><mfrac><mi>b2</mi><mi>c1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b13</mi><mo>=</mo><mfrac><mi>b3</mi><mi>c1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b14</mi><mo>=</mo><mfrac><mi>b4</mi><mi>c2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b15</mi><mo>=</mo><mfrac><mi>b5</mi><mi>c2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>b1</mi><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mfrac><mi>b2</mi><mi>c1</mi></mfrac><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mfrac><mi>b3</mi><mi>c1</mi></mfrac><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mfrac><mi>b4</mi><mi>c2</mi></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mi>b5</mi><mi>c2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>,</mo><mi>a_5</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>9</mn><mo>,</mo><mo>-</mo><mn>16</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>3</mn><mn>7</mn></mfrac><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mfrac><mn>16</mn><mn>7</mn></mfrac><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn><mo>,</mo><mn>14</mn><mo>,</mo><mn>10</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mfrac><mn>10</mn><mn>7</mn></mfrac><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mfrac><mn>2</mn><mn>9</mn></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>re_01</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>74</mn><mn>7</mn></mfrac><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mfrac><mn>6</mn><mn>7</mn></mfrac><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mfrac><mn>25</mn><mn>9</mn></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mn>5</mn><mn>3</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> P(x) + Q(x) = (#a11+#b11) x4 + (#a12+#b12) x3 + (#a13+#b13) x2 + (#a14+#b14) x+ (#a15+#b15) 

ÉS MILLOR SI SUMEU LES FRACCIONS SENSE CALCULADORA

]]> 1.2.1.20DT SUBTRACCIÓ POLINOMIS  

Subtracció de polinomis
Per restar el polinomi Q(x) del polinomi P(x), restem dels monomis de P(x) els monomis de mateix grau de Q(x).

Exemple:
(-2x4 + 7x3+ 6x2 + 3x - 1) - (-5x4- 6x2 + 3x - 5) = 3x4 + 7x3+ 12x2+ 4
Perquè:
-2x4 - (-5x4) = 3x4
7x3 - 0= 7x3
6x2- (- 6x2) = 12x2
3x - 3x = 0x (que no s'escriu)
- 1-(-5) = 4



]]> 0.0000000 0.0000000 0 1.2.1.21Q RestarG4G4 Amb els polinomis
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«/mrow»«/mstyle»«/math»
i «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«/mrow»«/mstyle»«/math»
Resta P(x) — Q(x)

Format de la resposta: 3x^2-5x+1

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>a1</mi><mo>∨</mo><mi>b1</mi><mo>≠</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a3</mi><mo>∨</mo><mi>b3</mi><mo>≠</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a5</mi><mo>∨</mo><mi>b5</mi><mo>≠</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a2</mi><mo>*</mo><mi>b2</mi><mo>≠</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a4</mi><mo>*</mo><mi>b4</mi><mo>≠</mo><mn>0</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>a1</mi><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mi>a2</mi><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mi>a3</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>a4</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>b1</mi><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mi>b2</mi><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mi>b3</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b4</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>12</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1. Escriu l'oposat del segon polinomi (canvia tots els seus signes)

       «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/mrow»«/mstyle»«/math»


2. Resta = suma aquest oposat

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

També ho pots fer directament

]]> 1.2.1.25Q RestarCoefFraccionaris Amb els polinomis
P(x) = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«/mrow»«/mstyle»«/math»
i Q(x) = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«/mrow»«/mstyle»«/math»
Calcula P(x) – Q(x)


]]>  

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a11</mi><mo>=</mo><mfrac><mi>a1</mi><mi>c1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a12</mi><mo>=</mo><mfrac><mi>a2</mi><mi>c2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a13</mi><mo>=</mo><mfrac><mi>a3</mi><mi>c1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a14</mi><mo>=</mo><mi>a4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a15</mi><mo>=</mo><mfrac><mi>a5</mi><mi>c2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mi>a1</mi><mi>c1</mi></mfrac><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mfrac><mi>a2</mi><mi>c2</mi></mfrac><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mfrac><mi>a3</mi><mi>c1</mi></mfrac><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>a4</mi><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mi>a5</mi><mi>c2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b11</mi><mo>=</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b12</mi><mo>=</mo><mfrac><mi>b2</mi><mi>c1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b13</mi><mo>=</mo><mfrac><mi>b3</mi><mi>c1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b14</mi><mo>=</mo><mfrac><mi>b4</mi><mi>c2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b15</mi><mo>=</mo><mfrac><mi>b5</mi><mi>c2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>b1</mi><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mfrac><mi>b2</mi><mi>c1</mi></mfrac><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mfrac><mi>b3</mi><mi>c1</mi></mfrac><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mfrac><mi>b4</mi><mi>c2</mi></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mi>b5</mi><mi>c2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>,</mo><mi>a_5</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>9</mn><mo>,</mo><mo>-</mo><mn>16</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>3</mn><mn>7</mn></mfrac><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mfrac><mn>16</mn><mn>7</mn></mfrac><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn><mo>,</mo><mn>14</mn><mo>,</mo><mn>10</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mfrac><mn>10</mn><mn>7</mn></mfrac><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mfrac><mn>2</mn><mn>9</mn></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>re_01</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>74</mn><mn>7</mn></mfrac><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mfrac><mn>6</mn><mn>7</mn></mfrac><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mfrac><mn>25</mn><mn>9</mn></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mn>5</mn><mn>3</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> P(x) + Q(x) = (#a11-#b11) x4 + (#a12-#b12) x3 + (#a13-#b13) x2 + (#a14-#b14) x+ (#a15-#b15) 

ÉS MILLOR SI RESTEULES FRACCIONS SENSE CALCULADORA

]]> 1.2.1.30DT MULTIPLICACIÓ X MONOMI  

Multiplicació per un monomi
Per a multiplicar el polinomi P(x) pel monomi Q(x) multipliquem TOTS els monomis de P(x) per Q(x). Agrupem i ordenem.

Exemple:
(-2x2)·(7x3+ 2x - 1) = (-2x2)· 7x3 + (-2x2)·2x + (-2x2)·(-1) 
= -14x5- 4x3+ 2x2



 
]]> 0.0000000 0.0000000 0 1.2.1.31Q G1G2 MonomixPolinomi Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math»


]]> 1.0000000 0.5000000 0 0 #re_01 <question><wirisCasSession>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_3&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_4&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_5&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;b_1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;b_2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;b_3&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;b_4&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;b_5&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_3&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;b_3&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;b_4&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;b_5&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;re_01&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_3&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_4&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_5&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;8&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;8&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;b_1&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b_2&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b_3&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b_4&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b_5&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;re_01&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;15&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;18&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml"> #re_01 </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> Cal multiplicar el MONOMI per CADA MONOMI del polinomi.

]]> 1.2.1.32Q G1G3 MonomixPolinomi Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math»


]]> 1.0000000 0.5000000 0 0 #re_01 <question><wirisCasSession>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_3&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_4&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mfenced&gt;&lt;mfenced close=&quot;}&quot; open=&quot;{&quot;&gt;&lt;mtable align=&quot;center&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mfenced&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math 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xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;28&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;35&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;8&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;63&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;49&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml"> #re_01 </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> Cal multiplicar el MONOMI per CADA MONOMI del polinomi.

]]> 1.2.1.33Q GnG4 MonomixPolinomi Calcula  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math»


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xmlns="http://www.w3.org/1998/Math/MathML"><mi>c4</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>b4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c5</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>b5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n5</mi><mo>=</mo><mi>n</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>,</mo><mi>a_5</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>,</mo><mi>a_5</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>6</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>-</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>*</mo><msup><mi>x</mi><mn>10</mn></msup><mo>+</mo><mn>20</mn><mo>*</mo><msup><mi>x</mi><mn>9</mn></msup><mo>-</mo><mn>20</mn><mo>*</mo><msup><mi>x</mi><mn>8</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>7</mn></msup><mo>+</mo><mn>36</mn><mo>*</mo><msup><mi>x</mi><mn>6</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Cal multiplicar el MONOMI per CADA MONOMI del polinomi:

#a · (#b) =

(#a1·x#n) · (#b1·x4)

+ (#a1·x#n) · (#b2·x3)

+  (#a1·x#n) · (#b3·x2)

+  (#a1·x#n) · (#b4·x)

+  (#a1·x#n) · (#b5)

]]> #a · (#b) =

    (#a1·x#n) · (#b1·x4)        = #c1 · x#n1

+ (#a1·x#n) · (#b2·x3)         = #c2 · x#n2

+  (#a1·x#n) · (#b3·x2)        = #c3 ·x#n3

+  (#a1·x#n) · (#b4·x)          = #c4 · x#n4

+  (#a1·x#n) · (#b5)              = #c5 · x#n5

]]> 1.2.1.40DT: MULTIPLICACIÓ POLINOMIS  

Multiplicació de 2 polinomis
Per a multiplicar el polinomi P(x) pel polinomi Q(x) multipliquem TOTS els monomis de P(x) per TOTS els monomis de Q(x). Agrupem i ordenem.

Exemple:
(-2x2+3x)·(7x3+ 2x - 1)= (-2x2)· 7x3 + (-2x2)·2x + (-2x2)·(-1) + 3x·7x3 + 3x·2x + 3x·(- 1)
= -14x5- 4x3+ 2x2 + 21x3+ 6x2- 3x
Agrupat i ordenat: -14x5 + 17x3 + 8x2 - 3x



 
]]> 0.0000000 0.0000000 0 1.2.1.41Q G2G2ProdPolinomis Amb els polinomis  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«/mrow»«/mstyle»«/math»
Multiplica  P(x) · Q(x)



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xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;b_1&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b_2&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b_3&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b_4&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b_5&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;8&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;8&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;re_01&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml"> #re_01 </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> Cal multiplicar CADA MONOMI del primer per CADA MONOMI del segon i ordenar i agrupar els monomis per graus.

]]> 1.2.1.42Q G2G3 ProdPolinomis Amb els polinomis       «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«/mstyle»«/math»
Multiplica  P(x) · Q(x)


]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>a_3</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>a_4</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>b_2</mi><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mi>b_3</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b_4</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>a_3</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>a_4</mi><mo>*</mo><mi>x</mi><mo>*</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>a_5</mi><mo>*</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>,</mo><mi>a_5</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>x</mi><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>re_01</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Multiplica  CADA MONOMI del primer per CADA MONOMI del segon;  ordena i agrupa els monomis per graus:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»5«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«/mstyle»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»5«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«/mstyle»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

Ara ordena i agrupa els monomis per graus.

 

]]> 1.2.1.43Q G3G3 ProdPolinomis Amb els polinomis
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«/mstyle»«/math»
Multiplica  P(x) · Q(x)


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xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_3&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_4&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_5&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math 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xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;8&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;re_01&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml"> #re_01 </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> Cal multiplicar CADA MONOMI del primer per CADA MONOMI del segon i ordenar i agrupar els monomis per graus.

]]> 1.2.1.44 G3G3 Frac ProduPolinomis Amb els polinomis
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«/mrow»«/mstyle»«/math»
i «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«/mrow»«/mstyle»«/math»
Multiplica P(x) · Q(x)


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xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;8&lt;/mn&gt;&lt;mn&gt;49&lt;/mn&gt;&lt;/mfrac&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;8&lt;/mn&gt;&lt;mn&gt;63&lt;/mn&gt;&lt;/mfrac&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;43&lt;/mn&gt;&lt;mn&gt;49&lt;/mn&gt;&lt;/mfrac&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;41&lt;/mn&gt;&lt;mn&gt;63&lt;/mn&gt;&lt;/mfrac&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;2822&lt;/mn&gt;&lt;mn&gt;3969&lt;/mn&gt;&lt;/mfrac&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mn&gt;63&lt;/mn&gt;&lt;/mfrac&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mn&gt;81&lt;/mn&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml"> #re_01 </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> Cal multiplicar CADA MONOMI del primer per CADA MONOMI del segon i ordenar i agrupar els monomis per graus.

]]> 1.2.1.45Q G4G4 ProdPolinomis Amb els polinomis  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«/mrow»«/mstyle»«/math»
Multiplica  P(x) · Q(x)


]]> Cal multiplicar CADA MONOMI del primer per CADA MONOMI del segon i ordenar i agrupar els monomis per graus.

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xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml"> #re_01 </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> 1.2.1.50DT OPERACIONS COMBINADES  

Operacions combinades

Quan cal efectuar operacions combinades, cal tenir present

  • l'ordre de les operacions és: Parèntesis (o claus, o claudàtors), Potències, Multiplicacions i divisions, Addicions i Subtraccions
  • l'ús de les identitats notables; (a+b)2 = a2 + 2ab + b2 i (a+b)(a-b)=a2 - b2



 
]]> 0.0000000 0.0000000 0 1.2.1.51Q ProducteSuma Donats els polinomis «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»p«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»R«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«/mrow»«/mstyle»«/math»
calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»sig«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»R«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«/mstyle»«/math»

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xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>5</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>13</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>11</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qr</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>5</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>11</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>16</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>9</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sig</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>resta</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer es calcula el producte Q(x) · R(x) = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»qr«/mi»«/mstyle»«/math»

Després es fa la #r11:   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»sig«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»R«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»sig«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»qr«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mstyle»«/math»

]]> 1.2.1.52Q ParentResta Donats els polinomis «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»p«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»R«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«/mrow»«/mstyle»«/math»
Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»[«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»R«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»]«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«/mrow»«/mstyle»«/math»


]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cp</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cq</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cr</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>coefp</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>cp</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cp</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cp</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cp</mi><mo>(</mo><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>coefq</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>cq</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cq</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cq</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cq</mi><mo>(</mo><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>coefr</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>cr</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cr</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cr</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cr</mi><mo>(</mo><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><msub><mi>coefp</mi><mn>1</mn></msub><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><msub><mi>coefp</mi><mn>2</mn></msub><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msub><mi>coefp</mi><mn>3</mn></msub><mo>*</mo><mi>x</mi><mo>+</mo><msub><mi>coefp</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><msub><mi>coefq</mi><mn>1</mn></msub><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><msub><mi>coefq</mi><mn>2</mn></msub><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msub><mi>coefq</mi><mn>3</mn></msub><mo>*</mo><mi>x</mi><mo>+</mo><msub><mi>coefq</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><msub><mi>coefr</mi><mn>1</mn></msub><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><msub><mi>coefr</mi><mn>2</mn></msub><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msub><mi>coefr</mi><mn>3</mn></msub><mo>*</mo><mi>x</mi><mo>+</mo><msub><mi>coefr</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p</mi><mo>-</mo><mo>(</mo><mi>q</mi><mo>+</mo><mi>r</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qr</mi><mo>=</mo><mi>q</mi><mo>+</mo><mi>r</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer s'efectua el claudàtor: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»R«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»qr«/mi»«/mrow»«/mstyle»«/math»

Després es fa la resta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«mrow»«mi mathvariant=¨bold¨»Q«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»R«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»p«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»qr«/mi»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

]]> 1.2.1.53Q PotènciaSuma Donats els polinomis «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»p«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»q«/mi»«/mrow»«/mstyle»«/math» calcula  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»sig«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»[«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«msup mathcolor=¨#003300¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»]«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«/mstyle»«/math».

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cp</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cq</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>coefp</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>cp</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cp</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cp</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cp</mi><mo>(</mo><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>coefq</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>cq</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cq</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cq</mi><mo>(</mo><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><msub><mi>coefp</mi><mn>1</mn></msub><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><msub><mi>coefp</mi><mn>2</mn></msub><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msub><mi>coefp</mi><mn>3</mn></msub><mo>*</mo><mi>x</mi><mo>+</mo><msub><mi>coefp</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><msub><mi>coefq</mi><mn>1</mn></msub><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msub><mi>coefq</mi><mn>2</mn></msub><mo>*</mo><mi>x</mi><mo>+</mo><msub><mi>coefq</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>s</mi><mo>=</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mi>p</mi><mo>+</mo><msup><mi>q</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>sig</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>w1</mi><mo>=</mo><mo>&quot;</mo><mi>suma</mi><mo>&quot;</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mi>p</mi><mo>-</mo><msup><mi>q</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>sig</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>w1</mi><mo>=</mo><mo>&quot;</mo><mi>resta</mi><mo>&quot;</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi><mo>=</mo><msup><mi>q</mi><mn>2</mn></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>16</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>12</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>20</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>13</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi></math></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer es fa la potència: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#0000FF¨»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«mrow»«mi mathvariant=¨bold¨»Q«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»q«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/mrow»«/mstyle»«/math»

Després es fa la #w1:  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»sig«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msup mathcolor=¨#0000FF¨»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«mrow»«mi mathvariant=¨bold¨»Q«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»p«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»sig«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

]]> 1.2.1.54Q ParentProducte Donats els polinomis «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»p«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»R«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«/mrow»«/mstyle»«/math»
Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»[«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»R«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»]«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«/mstyle»«/math»


]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cp</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cq</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cr</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>coefp</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>cp</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cp</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cp</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cp</mi><mo>(</mo><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>coefq</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>cq</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cq</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cq</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cq</mi><mo>(</mo><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>coefr</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>cr</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cr</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cr</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cr</mi><mo>(</mo><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><msub><mi>coefp</mi><mn>2</mn></msub><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msub><mi>coefp</mi><mn>3</mn></msub><mo>*</mo><mi>x</mi><mo>+</mo><msub><mi>coefp</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><msub><mi>coefq</mi><mn>2</mn></msub><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msub><mi>coefq</mi><mn>3</mn></msub><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><msub><mi>coefr</mi><mn>2</mn></msub><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msub><mi>coefr</mi><mn>3</mn></msub><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p</mi><mo>*</mo><mo>(</mo><mi>q</mi><mo>+</mo><mi>r</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qr</mi><mo>=</mo><mi>q</mi><mo>+</mo><mi>r</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer s'efectua el claudàtor: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»R«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»qr«/mi»«/mrow»«/mstyle»«/math»

Després es fa el producte: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«mrow»«mi mathvariant=¨bold¨»Q«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»R«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»p«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»qr«/mi»«/mrow»«/mfenced»«/mstyle»«/math»

]]> 1.2.1.55Q IdRem Efectua: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»p«/mi»«msup mathcolor=¨#003300¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cp</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cq</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cr</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>coefp</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>cp</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cp</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cp</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cp</mi><mo>(</mo><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>coefq</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>cq</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cq</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cq</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cq</mi><mo>(</mo><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>coefr</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>cr</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cr</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cr</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cr</mi><mo>(</mo><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><msub><mi>coefp</mi><mn>3</mn></msub><mo>*</mo><mi>x</mi><mo>+</mo><msub><mi>coefp</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><msub><mi>coefq</mi><mn>3</mn></msub><mo>*</mo><mi>x</mi><mo>+</mo><msub><mi>coefq</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><msub><mi>coefq</mi><mn>3</mn></msub><mo>*</mo><mi>x</mi><mo>-</mo><msub><mi>coefq</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><msup><mi>p</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qr</mi><mo>=</mo><mi>q</mi><mo>*</mo><mi>r</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p2</mi><mo>-</mo><mi>qr</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>20</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qr</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>16</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>20</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer es calcula la potència com a quadrat d'una suma: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#0000FF¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»p«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/mrow»«/mstyle»«/math»

després el producte com a diferència de quadrats:   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»qr«/mi»«/mstyle»«/math»

Després es fa la resta:   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow mathcolor=¨#0000FF¨»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»qr«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mstyle»«/math»

]]> 1.2.1.56Q IdRemPotG2G2 Efectua: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»p«/mi»«msup mathcolor=¨#003300¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cp</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cq</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cr</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>coefp</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>cp</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cp</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cp</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cp</mi><mo>(</mo><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>coefq</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>cq</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cq</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cq</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cq</mi><mo>(</mo><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><msub><mi>coefp</mi><mn>2</mn></msub><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msub><mi>coefp</mi><mn>3</mn></msub><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><msub><mi>coefq</mi><mn>2</mn></msub><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mo>&nbsp;</mo><msub><mi>coefq</mi><mn>3</mn></msub><mo>*</mo><mi>x</mi><mo>+</mo><msub><mi>coefq</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><msup><mi>p</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi><mo>=</mo><msup><mi>q</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p2</mi><mo>-</mo><mi>q2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>18</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>13</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer es calcula la potència com a quadrat d'una suma: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#0000FF¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»p«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/mrow»«/mstyle»«/math»

després la potència com un producte:   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»q«/mi»«msup»«mo mathvariant=¨bold¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»q«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«/mstyle»«/math»

Després es fa la resta:   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow mathcolor=¨#0000FF¨»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mstyle»«/math»

]]> 1.2.1.57Q ddqClaudàtorG2G2 Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mfenced mathcolor=¨#003300¨ open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»r«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfenced»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cp</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cq</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cr</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>coefp</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>cp</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cp</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cp</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cp</mi><mo>(</mo><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>coefq</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>cq</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cq</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cq</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cq</mi><mo>(</mo><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>coefr</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>cr</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cr</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cr</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>cr</mi><mo>(</mo><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><msub><mi>coefp</mi><mn>2</mn></msub><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msub><mi>coefp</mi><mn>3</mn></msub><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><msub><mi>coefp</mi><mn>2</mn></msub><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><msub><mi>coefp</mi><mn>3</mn></msub><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><msub><mi>coefq</mi><mn>2</mn></msub><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msub><mi>coefq</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><msub><mi>coefr</mi><mn>1</mn></msub><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msub><mi>coefr</mi><mn>2</mn></msub><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mi>p1</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qr</mi><mo>=</mo><mi>q</mi><mo>*</mo><mi>r</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p2</mi><mo>-</mo><mi>qr</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>,</mo><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>,</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>24</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>15</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qr</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>20</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>20</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>25</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer es calcula el claudàtor: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»qr«/mi»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

després, la diferència de quadrats:  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»p«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»12«/mn»«/mstyle»«/math»

Després es fa la resta:   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«mn mathvariant=¨bold¨»12«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»qr«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mstyle»«/math»

]]> 1.2.1.80MADT BINOMI NEWTON  

Binomi de Newton

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«msup mathcolor=¨#003300¨»«mo mathvariant=¨bold¨»)«/mo»«mi mathvariant=¨bold¨»n«/mi»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mfenced mathcolor=¨#003300¨»«mtable»«mtr»«mtd»«mi mathvariant=¨bold¨»n«/mi»«/mtd»«/mtr»«mtr»«mtd»«mn mathvariant=¨bold¨»0«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mfenced mathcolor=¨#003300¨»«mtable»«mtr»«mtd»«mi mathvariant=¨bold¨»n«/mi»«/mtd»«/mtr»«mtr»«mtd»«mn mathvariant=¨bold¨»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»a«/mi»«mrow»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»b«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mfenced mathcolor=¨#003300¨»«mtable»«mtr»«mtd»«mi mathvariant=¨bold¨»n«/mi»«/mtd»«/mtr»«mtr»«mtd»«mn mathvariant=¨bold¨»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#160;«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»a«/mi»«mrow»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mfenced mathcolor=¨#003300¨»«mtable»«mtr»«mtd»«mi mathvariant=¨bold¨»n«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#160;«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»b«/mi»«mrow»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mfenced mathcolor=¨#003300¨»«mtable»«mtr»«mtd»«mi mathvariant=¨bold¨»n«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»a«/mi»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»b«/mi»«mrow»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mfenced mathcolor=¨#003300¨»«mtable»«mtr»«mtd»«mi mathvariant=¨bold¨»n«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨»n«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»b«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msup»«/mrow»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»on«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mfenced mathcolor=¨#003300¨»«mtable»«mtr»«mtd»«mi mathvariant=¨bold¨»n«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨»k«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»!«/mo»«/mrow»«mrow»«mi mathvariant=¨bold¨»k«/mi»«mo mathvariant=¨bold¨»!«/mo»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»-«/mo»«mi mathvariant=¨bold¨»k«/mi»«mo mathvariant=¨bold¨»!«/mo»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«/mstyle»«/math»
 



 
]]> 0.0000000 0.0000000 0 1.2.1.81QMA GAleat Calcula   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»bp«/mi»«/mrow»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»ep«/mi»«/mrow»«/msup»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msup><mfenced><mrow><mi>a</mi><mo>·</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mi>n</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bp</mi><mo>=</mo><mi>a</mi><mo>·</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ep</mi><mo>=</mo><mi>n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n</mi><mo>=</mo><mn>3</mn></mrow><mrow><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n</mi><mo>=</mo><mn>4</mn></mrow><mrow><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mrow><mrow><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mrow></apply></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>81</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>324</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>486</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>324</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>81</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bp</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ep</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> El desenvolupament es fa amb els coeficients «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»L«/mi»«/mrow»«/mstyle»«/math»

 

]]> 1.2.1.82QMA nèsimTermeBinomi Calcula el #m1 monomi del desenvolupament de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»t«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»sig«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»ab«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»s«/mi»«/mrow»«/msup»«msup mathcolor=¨#003300¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/msup»«/mrow»«/mstyle»«/math».

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi>n</mi><mo>-</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>b</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mrow><mrow><mi>b</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>b</mi><mo>≠</mo><mo>-</mo><mn>1</mn><mo>∧</mo><mi>b</mi><mo>≠</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ab</mi><mo>=</mo><mfenced close="|" open="|"><mi>b</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>t</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>s</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>t</mi><mo>≠</mo><mi>s</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bnm</mi><mo>:</mo><mo>=</mo><msup><mi>ax</mi><mi>t</mi></msup><mo>+</mo><msup><mi>bx</mi><mi>s</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>sig</mi><mo>:</mo><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow><mrow><mi>sig</mi><mo>:</mo><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>m</mi><mo>=</mo><mn>2</mn></mrow><mrow><mi>m1</mi><mo>=</mo><mo>&quot;</mo><mn>2</mn><mi>n</mi><mo>&quot;</mo></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>m</mi><mo>=</mo><mn>3</mn></mrow><mrow><mi>m1</mi><mo>=</mo><mo>&quot;</mo><mn>3</mn><mi>r</mi><mo>&quot;</mo></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>m</mi><mo>=</mo><mn>4</mn></mrow><mrow><mi>m1</mi><mo>=</mo><mo>&quot;</mo><mn>4</mn><mi>t</mi><mo>&quot;</mo></mrow><mrow><mi>m1</mi><mo>=</mo><mi>m</mi><mo> </mo><mi>è</mi></mrow></apply></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>n</mi><mrow><mi>m</mi><mo>-</mo><mn>1</mn></mrow></apply><mo>·</mo><mo>(</mo><mi>a</mi><mo>·</mo><msup><mi>x</mi><mi>t</mi></msup><msup><mo>)</mo><mrow><mi>n</mi><mo>-</mo><mi>m</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>·</mo><msup><mfenced><mrow><mi>b</mi><mo>·</mo><msup><mi>x</mi><mi>s</mi></msup></mrow></mfenced><mrow><mi>m</mi><mo>-</mo><mn>1</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>n</mi><mrow><mi>m</mi><mo>-</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>n</mi><mo>-</mo><mi>m</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>m</mi><mo>-</mo><mn>1</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>è</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90720</mn><mo>*</mo><msup><mi>x</mi><mn>32</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">8</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> S'aplica el binomi de Newton.

El coeficient que procedeix del triangle de Pascal és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»c«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«/mrow»«/mstyle»«/math». 

Cal elevar «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#183;«/mo»«msup mathcolor=¨#000066¨»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»t«/mi»«/mrow»«/msup»«/mrow»«/mstyle»«/math» a «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»c«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»2«/mn»«/mrow»«/mstyle»«/math»  i   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»b«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«msup mathcolor=¨#000066¨»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»s«/mi»«/mrow»«/msup»«/mrow»«/mstyle»«/math»  a  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»c«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»3«/mn»«/mrow»«/mstyle»«/math»

]]> 1rBTX 02. POLINOMIS/1.2.2 Divisió de polinomis 1.2.2.10DT MÈTODE DE RUFFINI

]]> 0.0000000 0.0000000 0 1.2.2.11Q RuffiniG4 Calcula el quocient i el residu de la divisió següent emprant el mètode de Ruffini:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»:«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»d«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi»Q«/mi»«mo»=«/mo»«mn»2«/mn»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»-«/mo»«mn»5«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»3«/mn»«mi»x«/mi»«mo»-«/mo»«mn»7«/mn»«mspace linebreak=¨newline¨/»«mi»R«/mi»«mo»=«/mo»«mo»-«/mo»«mn»7«/mn»«/mrow»«/mstyle»«/math»

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]]> 1.0000000 0.5000000 0 0 Q=#QR=#R]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_3</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_4</mi><mo>)</mo><mo>+</mo><mi>a_5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p0</mi><mo>=</mo><msub><mi>P</mi><mn>0</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><msub><mi>P</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><msub><mi>P</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><msub><mi>P</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><msub><mi>P</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p_1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_3</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>a_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mfrac><mi>p_1</mi><mi>d</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>a_5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>=</mo><mi>a_1</mi><mo>*</mo><mi>p4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>b3</mi><mo>+</mo><mi>p3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>a_1</mi><mo>*</mo><mi>c3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>b2</mi><mo>+</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>a_1</mi><mo>*</mo><mi>c2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>b1</mi><mo>+</mo><mi>p1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b0</mi><mo>=</mo><mi>a_1</mi><mo>*</mo><mi>c1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c0</mi><mo>=</mo><mi>b0</mi><mo>+</mo><mi>p0</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>18</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>290</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>593</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>290</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p0</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>593</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>18</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>290</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>600</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>34</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>120</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mi>#Q</mi><mspace linebreak="newline"/><mi>R</mi><mo>=</mo><mi>#R</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="inputCompound">true</data><data name="casSession"/></localData></question>   #p4 #p3 #p2 #p1 #p0 #a_1   #b3 #b2 #b1 #b0   #p4 #c3 #c2 #c1 #c0 ]]> 1.2.2.12Q RuffiniG4_2 Calcula el quocient i el residu de la divisió següent emprant el mètode de Ruffini:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»:«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»d«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi»Q«/mi»«mo»=«/mo»«mn»2«/mn»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»-«/mo»«mn»5«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»3«/mn»«mi»x«/mi»«mo»-«/mo»«mn»7«/mn»«mspace linebreak=¨newline¨/»«mi»R«/mi»«mo»=«/mo»«mo»-«/mo»«mn»7«/mn»«/mrow»«/mstyle»«/math»

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]]> 1.0000000 0.5000000 0 0 Q=#QR=#R]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_3</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_4</mi><mo>)</mo><mo>+</mo><mi>a_5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p0</mi><mo>=</mo><msub><mi>P</mi><mn>0</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><msub><mi>P</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><msub><mi>P</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><msub><mi>P</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><msub><mi>P</mi><mn>4</mn></msub></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mi>#Q</mi><mspace linebreak="newline"/><mi>R</mi><mo>=</mo><mi>#R</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="inputCompound">true</data><data name="casSession"/></localData></question>   #p4 #p3 #p2 #p1 #p0 #a_1   #b3 #b2 #b1 #b0   #p4 #c3 #c2 #c1 #c0 ]]> 1.2.2.13Q RuffiniG5 Calcula el quocient i el residu de la divisió següent emprant el mètode de Ruffini:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»:«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»d«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi»Q«/mi»«mo»=«/mo»«mn»2«/mn»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»-«/mo»«mn»5«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»3«/mn»«mi»x«/mi»«mo»-«/mo»«mn»7«/mn»«mspace linebreak=¨newline¨/»«mi»R«/mi»«mo»=«/mo»«mo»-«/mo»«mn»7«/mn»«/mrow»«/mstyle»«/math»

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]]> 1.0000000 0.5000000 0 0 Q=#Q1R=#R1]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>42</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>36</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>36</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>38</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>144</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mo>#</mo><mi>Q</mi><mn>1</mn><mspace linebreak="newline"/><mi>R</mi><mo>=</mo><mo>#</mo><mi>R</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="inputCompound">true</data><data name="casSession"/></localData></question> Es va multiplicant i sumant.

 

]]> 1.2.2.15Q RuffiniG4 CoefNuls Calcula el quocient i el residude la divisió següent emprant el mètode de Ruffini:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»:«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨normal¨»Q«/mi»«mo»=«/mo»«mn»2«/mn»«msup»«mi mathvariant=¨normal¨»x«/mi»«mn»3«/mn»«/msup»«mo»-«/mo»«mn»5«/mn»«msup»«mi mathvariant=¨normal¨»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»3«/mn»«mi mathvariant=¨normal¨»x«/mi»«mo»-«/mo»«mn»7«/mn»«mspace linebreak=¨newline¨/»«mi mathvariant=¨normal¨»R«/mi»«mo»=«/mo»«mo»-«/mo»«mn»7«/mn»«/mrow»«/mstyle»«/math»

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]]> 1.0000000 0.5000000 0 0 Q=#QR=#R]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>a_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>a_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>P</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_3</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_4</mi><mo>)</mo><mo>+</mo><mi>a_5</mi></mtd></mtr><mtr><mtd><mi>p0</mi><mo>=</mo><msub><mi>P</mi><mn>0</mn></msub></mtd></mtr><mtr><mtd><mi>p1</mi><mo>=</mo><msub><mi>P</mi><mn>1</mn></msub></mtd></mtr><mtr><mtd><mi>p2</mi><mo>=</mo><msub><mi>P</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd><mi>p3</mi><mo>=</mo><msub><mi>P</mi><mn>3</mn></msub></mtd></mtr><mtr><mtd><mi>p4</mi><mo>=</mo><msub><mi>P</mi><mn>4</mn></msub></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mo>(</mo><mi>p2</mi><mo>=</mo><mn>0</mn><mo>)</mo><mo>∨</mo><mo>(</mo><mi>p3</mi><mo>=</mo><mn>0</mn><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p_1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_3</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>a_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mfrac><mi>p_1</mi><mi>d</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>a_5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>=</mo><mi>a_1</mi><mo>*</mo><mi>p4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>b3</mi><mo>+</mo><mi>p3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>a_1</mi><mo>*</mo><mi>c3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>b2</mi><mo>+</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>a_1</mi><mo>*</mo><mi>c2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>b1</mi><mo>+</mo><mi>p1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b0</mi><mo>=</mo><mi>a_1</mi><mo>*</mo><mi>c1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c0</mi><mo>=</mo><mi>b0</mi><mo>+</mo><mi>p0</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>40</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>34</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>40</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p0</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>34</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>40</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>32</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>32</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mi>#Q</mi><mspace linebreak="newline"/><mi>R</mi><mo>=</mo><mi>#R</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="inputCompound">true</data><data name="casSession"/></localData></question>   #p4 #p3 #p2 #p1 #p0 #a_1   #b3 #b2 #b1 #b0   #p4 #c3 #c2 #c1 #c0 ]]> 1.2.2.21Q D? amb d,q,r S'ha dividit el polinomi P(x) per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»d«/mi»«/mrow»«/mstyle»«/math». El residu és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»R«/mi»«/mrow»«/mstyle»«/math» i el quocient «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»Q«/mi»«/mrow»«/mstyle»«/math».

Quin és el polinomi P(x)?

Format de la resposta:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mn»2«/mn»«msup»«mi mathvariant=¨normal¨»x«/mi»«mn»3«/mn»«/msup»«mo»-«/mo»«mn»5«/mn»«msup»«mi mathvariant=¨normal¨»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»3«/mn»«mi mathvariant=¨normal¨»x«/mi»«mo»-«/mo»«mn»7«/mn»«/mrow»«/mstyle»«/math»

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]]> 1.0000000 0.5000000 0 0 #P <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_3</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_4</mi><mo>)</mo><mo>+</mo><mi>a_5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p0</mi><mo>=</mo><msub><mi>P</mi><mn>0</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><msub><mi>P</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><msub><mi>P</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><msub><mi>P</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><msub><mi>P</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p_1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_3</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>a_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mfrac><mi>p_1</mi><mi>d</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>a_5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>=</mo><mi>a_1</mi><mo>*</mo><mi>p4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>b3</mi><mo>+</mo><mi>p3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>a_1</mi><mo>*</mo><mi>c3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>b2</mi><mo>+</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>a_1</mi><mo>*</mo><mi>c2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>b1</mi><mo>+</mo><mi>p1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b0</mi><mo>=</mo><mi>a_1</mi><mo>*</mo><mi>c1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c0</mi><mo>=</mo><mi>b0</mi><mo>+</mo><mi>p0</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>18</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>290</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>593</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>290</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p0</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>593</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>18</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>290</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>600</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>34</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>120</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#P</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Es recorda que:

Dividend = quocient · divisor + residu

]]> 1.2.2.50DT DIVISIÓ CLÀSSICA

]]> 0.0000000 0.0000000 0 1.2.2.51Q Divisió G4G2 Exacte Efectua la divisió següent i determina el seu quocient

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»:«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»Q«/mi»«/mrow»«/mstyle»«/math»
]]> 1.0000000 0.5000000 0 0 #r_73]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p_0</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>p_0</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>p_1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>p_2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>p_3</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>p_4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>p_1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>p_2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_73</mi><mo>=</mo><mfrac><mi>P</mi><mi>Q</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>5</mn></msup><mo>-</mo><mn>52</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>494</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>2044</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3392</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1792</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>16</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_73</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>32</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>142</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>112</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>73</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1.2.2.52Q Divisió G4G2 Residu Efectua la divisió següent:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»:«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»Q«/mi»«/mrow»«/mstyle»«/math»
 
i determina el quocient (Q)  i el residu (R)
]]> 1.0000000 0.2500000 0 0 Q=#sol1R=#sol2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>p_0</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>p_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>p_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>p_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>p_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>p_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>p_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>P</mi><mo>=</mo><mi>p_0</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>p_1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>p_2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>p_3</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>p_4</mi><mo>)</mo><mo>+</mo><mi>p_5</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>p_6</mi></mtd></mtr><mtr><mtd><mi>Q</mi><mo>=</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>p_1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>p_2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>q1</mi><mo>=</mo><mi>p_0</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>P1</mi><mo>=</mo><mo>-</mo><mi>q1</mi><mo>*</mo><mi>Q</mi></mtd></mtr><mtr><mtd><mi>P2</mi><mo>=</mo><mi>P</mi><mo>+</mo><mi>P1</mi></mtd></mtr><mtr><mtd><mi>p3</mi><mo>=</mo><msub><mi>P2</mi><mn>3</mn></msub></mtd></mtr><mtr><mtd><mi>q2</mi><mo>=</mo><mi>q1</mi><mo>+</mo><mi>p3</mi><mo>*</mo><mi>x</mi></mtd></mtr><mtr><mtd><mi>P3</mi><mo>=</mo><mo>-</mo><mi>p3</mi><mo>*</mo><mi>x</mi><mo>*</mo><mi>Q</mi></mtd></mtr><mtr><mtd><mi>P4</mi><mo>=</mo><mi>P2</mi><mo>+</mo><mi>P3</mi></mtd></mtr><mtr><mtd><mi>p4</mi><mo>=</mo><msub><mi>P4</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd><mi>P5</mi><mo>=</mo><mo>-</mo><mi>p4</mi><mo>*</mo><mi>Q</mi></mtd></mtr><mtr><mtd><mi>P6</mi><mo>=</mo><mi>P4</mi><mo>+</mo><mi>P5</mi></mtd></mtr><mtr><mtd><mi>q3</mi><mo>=</mo><mi>q1</mi><mo>+</mo><mi>p3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>p4</mi></mtd></mtr></mtable><mrow><mfenced><mrow><mi>p3</mi><mo>≠</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>p4</mi><mo>≠</mo><mn>0</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>quocient</mi><mfenced><mrow><mi>P</mi><mo>,</mo><mi>Q</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>residu</mi><mfenced><mrow><mi>P</mi><mo>,</mo><mi>Q</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>30</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>63</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>114</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>315</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>x</mi><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>18</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>27</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>81</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>114</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>315</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>27</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>27</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>27</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>162</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>54</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>48</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>315</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>54</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>54</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>54</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>324</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P6</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>27</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>54</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>27</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>54</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>9</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>R</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question>   #P #Q #P1 #q1      #P2                       ]]>   #P #Q #P1 #q2    #P2      #P3       #P4      ]]>   #P #Q #P1 #q3    #P2      #P3        #P4    #P5    ]]> 1.2.2.53Q Divisió G4G1 Residu Efectua la divisió següent:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»:«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»Q«/mi»«/mrow»«/mstyle»«/math»
 
i determina el quocient (Q)  i el residu (R)
]]> 1.0000000 0.5000000 0 0 Q=#sol1R=#sol2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>p_0</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>p_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>p_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>p_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>p_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>p_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>p_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>P</mi><mo>=</mo><mi>p_0</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>p_1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>p_2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>p_3</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>p_4</mi><mo>)</mo><mo>+</mo><mi>p_5</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>p_6</mi></mtd></mtr><mtr><mtd><mi>Q</mi><mo>=</mo><mo>(</mo><mi>p_2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>p_1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>q1</mi><mo>=</mo><mi>p_0</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>P1</mi><mo>=</mo><mo>-</mo><mi>q1</mi><mo>*</mo><mi>Q</mi></mtd></mtr><mtr><mtd><mi>P2</mi><mo>=</mo><mi>P</mi><mo>+</mo><mi>P1</mi></mtd></mtr><mtr><mtd><mi>p3</mi><mo>=</mo><msub><mi>P2</mi><mn>3</mn></msub></mtd></mtr><mtr><mtd><mi>q2</mi><mo>=</mo><mi>q1</mi><mo>+</mo><mi>p3</mi><mo>*</mo><mi>x</mi></mtd></mtr><mtr><mtd><mi>P3</mi><mo>=</mo><mo>-</mo><mi>p3</mi><mo>*</mo><mi>x</mi><mo>*</mo><mi>Q</mi></mtd></mtr><mtr><mtd><mi>P4</mi><mo>=</mo><mi>P2</mi><mo>+</mo><mi>P3</mi></mtd></mtr><mtr><mtd><mi>p4</mi><mo>=</mo><msub><mi>P4</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd><mi>P5</mi><mo>=</mo><mo>-</mo><mi>p4</mi><mo>*</mo><mi>Q</mi></mtd></mtr><mtr><mtd><mi>P6</mi><mo>=</mo><mi>P4</mi><mo>+</mo><mi>P5</mi></mtd></mtr><mtr><mtd><mi>q3</mi><mo>=</mo><mi>q1</mi><mo>+</mo><mi>p3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>p4</mi></mtd></mtr></mtable><mrow><mfenced><mrow><mi>p3</mi><mo>≠</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>p4</mi><mo>≠</mo><mn>0</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>24</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>84</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>283</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>63</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>24</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>84</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mfrac><mn>51</mn><mn>16</mn></mfrac><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mfrac><mn>93</mn><mn>64</mn></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mn>1949</mn><mn>256</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3427</mn><mn>256</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>R</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question>  

 

]]> 1rBTX 02. POLINOMIS/1.2.3 Teorema del residu 1.2.3.10DT VALOR NUMÈRIC  
Valor numèric d'un polinomi

El valor numèric d'un polinomi s'obté substituint la indeterminada per un nombre concret.

Exemple: si P(x)=3x3 - 5x2 + 8x - 1,

P(-1) = 3·(-1)3 - 5·(-1)2 + 8·(-1) -1 = 3·(-1) - 5·1 + 8·(-1) -1 = -17

P(1) = 3 ·13 - 5 · 12 + 8 · 1 - 1 = 3 - 5 + 8 - 1 = 5

ATENCIÓ A L'ORDRE DE LES OPERACIONS:
potències, multiplicacions, sumes/restes
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 0.0000000 0.0000000 0 1.2.3.11Q ValorNumèricG1 Considera el polinomi P(x) = #a
Calcula el seu valor numèric quan x = #d que s'escriu P(#d).

Format: nombre enter

]]> 1.0000000 0.5000000 0 0 #re_01 <question><wirisCasSession>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_4&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_5&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_4&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_5&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;re_01&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_4&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_5&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_3&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_4&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_5&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_3&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;re_01&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;13&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml"> #re_01 </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> Substitueix  x pel nombre indicat i fes els càlculs.

]]> 1.2.3.12Q ValorNumèricG2 Considera el polinomi P(x) = #a
Calcula el seu valor numèric quan x = #d que s'escriu P(#d).

Format: nombre enter

]]> 1.0000000 0.5000000 0 0 #re_01 <question><wirisCasSession>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_3&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_4&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_5&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_3&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_4&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_5&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;re_01&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_3&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_4&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_5&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_3&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_4&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_5&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;re_01&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;41&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml"> #re_01 </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> Substitueix  x pel nombre indicat i fes els càlculs.

]]> 1.2.3.12VF PolinomiDivisor? #dvsr és un divisor de P(x) = #poli?

]]> 1.0000000 1.0000000 0 Vertader Fals <question><wirisCasSession>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;x1&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;x2&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;x3&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;poli&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;·&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;x1&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;·&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;x2&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;·&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;x3&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;dvsr&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;sol&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;·&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;x1&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;·&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;x2&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;·&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;x3&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;?&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;sol&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;cert&lt;/mi&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><localData><data name="cas">false</data></localData></question> 1.2.3.13Q ValorNumèricG3 Considera el polinomi P(x) = #a
Calcula el seu valor numèric quan x = #d que s'escriu P(#d).

Format: nombre enter.

]]> 1.0000000 0.5000000 0 0 #re_01 <question><wirisCasSession>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_3&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_4&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_5&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_3&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_4&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_5&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;re_01&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_3&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_4&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a_5&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_3&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_4&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_5&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;re_01&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;68&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml"> #re_01 </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> Substitueix  x pel nombre indicat i fes els càlculs... o fes servir el teorema del residu

]]> 1.2.3.14Q ValorNumèricG4 Considera el polinomi «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«/mrow»«/mstyle»«/math»
Calcula el seu valor numèric quan «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»d«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«/mrow»«/mstyle»«/math»que s'escriu «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»d«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«/mrow»«/mstyle»«/math»

Format: nombre enter.

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>a_1</mi><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mi>a_2</mi><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mi>a_3</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>a_4</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>a_1</mi><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mi>a_2</mi><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mi>a_3</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>a_4</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>d</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>,</mo><mi>a_5</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>-</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>649</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Es substitueix la x per #d i es fan els càlculs:
PRIMER les potències;
després les multiplicacions,
per últim, les sumes i restes.

També pots calcular el residu de la divisió per #w1

]]> 1.2.3.15Q ValorNumèricCoefFraccionaris Calcula el valor numèric del polinomi «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«/mrow»«/mstyle»«/math» per a «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»f«/mi»«/mrow»«/mstyle»«/math».

]]> 1.0000000 0.5000000 0 0 #r_67 <question><wirisCasSession>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;apply&gt;&lt;csymbol definitionURL=&quot;http://www.wiris.com/XML/csymbol&quot;&gt;repeat&lt;/csymbol&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mfrac&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd/&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;mod&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;≠&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/apply&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;apply&gt;&lt;csymbol definitionURL=&quot;http://www.wiris.com/XML/csymbol&quot;&gt;repeat&lt;/csymbol&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;c_1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;c_2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;c_3&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;c_4&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd/&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mrow&gt;&lt;mi&gt;c_1&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;c_2&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;c_3&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;c_4&lt;/mi&gt;&lt;mo&gt;≠&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/apply&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;·&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;c_1&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;·&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;c_2&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;·&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;c_3&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;c_4&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;r_67&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;·&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;c_1&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;·&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;c_2&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;·&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;c_3&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;c_4&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;21&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;48&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;39&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;r_67&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;5667&lt;/mn&gt;&lt;mn&gt;512&lt;/mn&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml"> #r_67 </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> Només cal substituir i efectuar. O aplicar el teorema del residu

]]> 1.2.3.50DT TEOREMA RESIDU  

Teorema del residu

El residu de la divisió d'un polinomi P(x) per x - a és igual al valor numèric del polinomi per x = a o sigui:

residu = P(a)



]]> 0.0000000 0.0000000 0 1.2.3.51VF Polinomi és múltiple? P(x) = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»poli«/mi»«/mrow»«/mstyle»«/math» és un múltiple de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»dvsr«/mi»«/mrow»«/mstyle»«/math»?

]]> 1.0000000 1.0000000 0 Vertader Fals Comprova si el residu de la divisió és zero

]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>poli</mi><mo>:</mo><mo>=</mo><mi>a</mi><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x1</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x2</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dvsr</mi><mo>:</mo><mo>=</mo><mi>x</mi><mo>-</mo><mi>r</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>:</mo><mo>=</mo><mo>(</mo><mi>a</mi><mo>·</mo><mo>(</mo><mi>r</mi><mo>-</mo><mi>x1</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>r</mi><mo>-</mo><mi>x2</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>r</mi><mo>-</mo><mi>x3</mi><mo>)</mo><mo>=</mo><mn>0</mn><mo>)</mo><mo>?</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cert</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 1.2.3.52VF PolinomiDivisible? P(x) = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»poli«/mi»«/mrow»«/mstyle»«/math» és divisible per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»dvsr«/mi»«/mrow»«/mstyle»«/math»?

]]> 1.0000000 1.0000000 0 Vertader Fals Calcula el residu (o el valor numèric) per saber si és nul

]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>poli</mi><mo>:</mo><mo>=</mo><mi>a</mi><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x1</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x2</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dvsr</mi><mo>:</mo><mo>=</mo><mi>x</mi><mo>-</mo><mi>r</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>:</mo><mo>=</mo><mo>(</mo><mi>a</mi><mo>·</mo><mo>(</mo><mi>r</mi><mo>-</mo><mi>x1</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>r</mi><mo>-</mo><mi>x2</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>r</mi><mo>-</mo><mi>x3</mi><mo>)</mo><mo>=</mo><mn>0</mn><mo>)</mo><mo>?</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fals</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 1.2.3.61Q ComprovaTeoremaResidu Considera el polinomi «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«/mrow»«/mstyle»«/math»
a) Calcula el residu R de la divisió per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«/mrow»«/mstyle»«/math». 
b) Calcula el valor numèric del polinomi P per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«/mrow»«/mstyle»«/math».


]]> 1.0000000 0.5000000 0 0 R=#r_1P =#r_1]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>-</mo><mi>a</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mfenced><mrow><mi>a_4</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_3</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>)</mo></mrow></mfenced><mo>+</mo><mi>r_1</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mo>#</mo><mi>r</mi><mi>_</mi><mn>1</mn><mspace linebreak="newline"/><mi>P</mi><mo>&#160;</mo><mo>=</mo><mo>#</mo><mi>r</mi><mi>_</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Tant si divideixes per #b, com si calcules P(#a) el resultat és el mateix.

]]> 1.2.3.71Q Trobar z (G1)/P(G4) divisible per x-a Troba el valor de z tal que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«/mrow»«/mstyle»«/math» sigui divisible per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»Q«/mi»«/mrow»«/mstyle»«/math»


]]> 1.0000000 0.5000000 0 0 #R_1 <question><wirisCasSession>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_0&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_3&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_4&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;a_4&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;a_3&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;R_1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_0&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_3&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_4&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;18&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;38&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;18&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;37&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;R_1&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml"> #R_1 </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> Cal fer la divisió i igualar el residu a zero. També es pot calcular el valor numèric per x = #a.

]]> 1.2.3.72Q Trobar k (G0)/P(G3)Divisible(x-a) Calcula el valor del terme independent k del polinomi «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«/mrow»«/mstyle»«/math» perquè, en dividir-lo entre «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»D«/mi»«/mrow»«/mstyle»«/math», la divisió sigui exacta.

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>n</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mrow><mrow><mi>n</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>:</mo><mo>=</mo><mfrac><mi>n</mi><mi>d</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>:</mo><mo>=</mo><mi>a</mi><mo>·</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mo>&quot;</mo><mi>k</mi><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>:</mo><mo>=</mo><mi>x</mi><mo> </mo><mo>-</mo><mi>r</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>:</mo><mo>=</mo><mo>-</mo><mo>(</mo><mi>a</mi><mo>·</mo><msup><mi>r</mi><mn>3</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><msup><mi>r</mi><mn>2</mn></msup><mo>+</mo><mi>c</mi><mo>*</mo><mi>r</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>+</mo><ms>k</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>8</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Fes la divisió i iguala el residu a zero.

]]> 1.2.3.73Q Troba z (G2)/P(G4) Múltiple(x-a) Troba el valor de z tal que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«/mrow»«/mstyle»«/math» sigui múltiple de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨»Q«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»Q«/mi»«/mrow»«/mstyle»«/math»


]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a0</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mo> </mo><mi>a4</mi><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mi>a3</mi><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mi>z</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>a1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a0</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>residu</mi><mo>(</mo><mi>P</mi><mo>,</mo><mi>Q</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>resol</mi><mfenced><mrow><mi>r1</mi><mo>=</mo><mn>0</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><mi>R</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>a_0</mi><mo>,</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mi>a_0</mi><mo>,</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><mi>z</mi><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><mi>z</mi><mo>-</mo><mn>143</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mi>x</mi><mo>,</mo><mi>z</mi><mo>=</mo><mfrac><mn>143</mn><mn>9</mn></mfrac></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>143</mn><mn>9</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> La divisió té per residu #r1, i cal que aquest residu sigui igual a zero.

També es pot calcular el valor numèric per x = #a, i dona P(#a) = #r1

]]> 1.2.3.74Q Trobar k/ divisió P(x) per x-a ResiduDonat Quin ha de ser el valor del coeficient k perquè el residu de la divisió del polinomi «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»poli«/mi»«/mrow»«/mstyle»«/math» entre «math style=¨font-family:Arial¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»dvsr«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»sigui«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«/mstyle»«/math»?]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;20&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;20&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;apply&gt;&lt;csymbol definitionURL=&quot;http://www.wiris.com/XML/csymbol&quot;&gt;repeat&lt;/csymbol&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;≠&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/apply&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;poli&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;·&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;·&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;dvsr&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;sol&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;poli&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;dvsr&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;sol&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;17&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml"> #sol </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> Es calcula el residu i s'iguala a #r.

]]> 1rBTX 02. POLINOMIS/1.2.4 Factorització 1.2.4.10DT FACTORITZAR POLI SENSE TIND  

Factoritzar polinomi

sense terme independent
Si un polinomi  no té terme independent, es treu x en factor amb el màxim grau possible.
Exemple:
-2x4 + 7x3+ 6x2 = x2 · (-2x2 + 7x + 6) 



]]> 0.0000000 0.0000000 0 1.2.4.11Q Treu x FComú Treu x en factor en polinomi «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: x2(2x2+x+6)

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></mtd></mtr></mtable><mrow><mfenced><mrow><mi>d</mi><mo>&lt;</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><msup><mi>x</mi><mi>n</mi></msup><mo>*</mo><mi>Q</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>P</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>6</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>5</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>4</mn></msup><mo>*</mo><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que el polinomi no té terme independent, es pot treure x#n en factor comú:

x#n ·(#Q)

#Q no es pot factoritzar perquè té un discriminant negatiu.

]]> 1.2.4.12Q Treu x FComú Gn Factoritza el polinomi P(x) = #P

Format de la resposta: x2(2x2+x+6)

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></mtd></mtr></mtable><mrow><mi>d</mi><mo>&lt;</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><msup><mi>x</mi><mi>n</mi></msup><mo>*</mo><mi>Q</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>P</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>6</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>5</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>4</mn></msup><mo>*</mo><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que el polinomi no té terme independent, es pot treure x#n en factor comú:

x#n ·(#Q)

#Q no es pot factoritzar ja que té discriminant negatiu.

 

]]> 1.2.4.20DT FACTORITZAR IDREMARCABLE  

Factoritzar polinomi

amb identitat remarcable

Abans de començar càlculs val la pena comprovar si el polinomi no es pot escriure com una identitat remarcable.
Exemples:
5x2+ 20x+ 20 = 5 · (x2 + 4x + 4) = 5·(x+2)2

-2x2 + 50 = -2·(x2 - 25) =  -2(x+5)(x-5)



]]> 0.0000000 0.0000000 0 1.2.4.21Q Factoritza DDQ Factoritza el polinomi «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: 4(x+2)(x-2)

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi><mo>=</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>P</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>a1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>,</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>80</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Es pot treure #a en factor comú per posar en evidència la diferència de quadrats: 

#P = #a · (#P1)

]]> 1.2.4.22Q Factoritza DDQ_2 Factoritza el polinomi «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: 4(x+2)(x-2)

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi><mo>=</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>P</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>a1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>,</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>80</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Es pot treure #a en factor comú per posar en evidència la diferència de quadrats: 

#P = #a · (#P1)

]]> 1.2.4.25Q Factoritza QPerfecte Factoritza el polinomi P(x) = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: 4(x-1)^2

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a1</mi><msup><mo>)</mo><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi><mo>=</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a1</mi><msup><mo>)</mo><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>P</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>a1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>,</mo><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>30</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>45</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfenced><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Es pot treure #a en factor comú per posar en evidència el quadrat d'un binomi: 

#P = #a · (#P1)

]]> 1.2.4.26Q FactoritzaQPerfecte Factoritza el polinomi «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: 4(x-1)^2

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a1</mi><msup><mo>)</mo><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi><mo>=</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a1</mi><msup><mo>)</mo><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>P</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>a1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>,</mo><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>30</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>45</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfenced><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Es pot treure #a en factor comú per posar en evidència el quadrat d'un binomi: 

#P = #a · (#P1)

]]> 1.2.4.30DT FACTORITZA G2 a,x1,x2  

Factoritzar polinomi 2n grau amb solucions

Si un polinomi  de grau 2 té solucions, es pot escriure: 

ax2 + bx + c = a (x - x1)(x - x2)

Atenció: no et deixis la a!

 

]]> 0.0000000 0.0000000 0 1.2.4.31Q Factoritza G2 Factoritza el polinomi «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: 4(x+2)(x-1)

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>a1</mi><mo>≠</mo><mi>a2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>a1</mi><mo>+</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>a1</mi><mo>*</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>P</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>36</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>36</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>441</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Es pot factoritzar calculant les arrels amb el discriminant:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#916;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«msup mathcolor=¨#0000FF¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»d«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#177;«/mo»«msqrt»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/msqrt»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8660;«/mo»«mfenced mathcolor=¨#0000FF¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»La«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»factoritzaci§#243;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#233;s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»ax«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»bx«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»NO«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»OBLIDIS«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»DE«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»POSAR«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»LA«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»a«/mi»«/math»

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Format de la resposta: 4(x+2)(x-1)

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>a1</mi><mo>≠</mo><mi>a2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>a1</mi><mo>+</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>a1</mi><mo>*</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>P</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>36</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>36</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>441</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Es pot factoritzar calculant les arrels amb el discriminant:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#916;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«msup mathcolor=¨#0000FF¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»d«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#177;«/mo»«msqrt»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/msqrt»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8660;«/mo»«mfenced mathcolor=¨#0000FF¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»La«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»factoritzaci§#243;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#233;s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»ax«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»bx«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»NO«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»OBLIDIS«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»DE«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»POSAR«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»LA«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»a«/mi»«/math»

]]> 1.2.4.40DT FACTORITZA RUFFINI  

Factoritzar un polinomi amb la regla de Ruffini

Si un polinomi  té terme independent i grau superior a 2, es va dividint per (x - a) fins al grau 2 pel mètode de Ruffini.
Valor de a: cal provar-ho amb tots els divisors del terme independent, ORDENADAMENT I REPETINT-LOS SI ES POT. Si el terme independent és 12, a pot ser igual a  ±1,±2,±3,±4,±6,±12. 

Exemple: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#000033¨»«mi mathcolor=¨#000033¨»x«/mi»«mn»4«/mn»«/msup»«mo mathcolor=¨#000033¨»-«/mo»«mn mathcolor=¨#000033¨»5«/mn»«msup mathcolor=¨#000033¨»«mi mathcolor=¨#000033¨»x«/mi»«mn»3«/mn»«/msup»«mo mathcolor=¨#000033¨»+«/mo»«mn mathcolor=¨#000033¨»20«/mn»«mi mathcolor=¨#000033¨»x«/mi»«mo mathcolor=¨#000033¨»-«/mo»«mn mathcolor=¨#000033¨»16«/mn»«/mrow»«/mstyle»«/math». Ruffini dona com arrels 1 i 2. El quocient de 2n grau té per solucions: -2 i 4:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#000033¨»«mi mathvariant=¨normal¨ mathcolor=¨#000033¨»x«/mi»«mn»4«/mn»«/msup»«mo mathcolor=¨#000033¨»-«/mo»«mn mathcolor=¨#000033¨»5«/mn»«msup mathcolor=¨#000033¨»«mi mathvariant=¨normal¨ mathcolor=¨#000033¨»x«/mi»«mn»3«/mn»«/msup»«mo mathcolor=¨#000033¨»+«/mo»«mn mathcolor=¨#000033¨»20«/mn»«mi mathvariant=¨normal¨ mathcolor=¨#000033¨»x«/mi»«mo mathcolor=¨#000033¨»-«/mo»«mn mathcolor=¨#000033¨»16«/mn»«mo mathcolor=¨#000033¨»=«/mo»«mo mathcolor=¨#000033¨»(«/mo»«mi mathvariant=¨normal¨ mathcolor=¨#000033¨»x«/mi»«mo mathcolor=¨#000033¨»+«/mo»«mn mathcolor=¨#000033¨»2«/mn»«mo mathcolor=¨#000033¨»)«/mo»«mo mathcolor=¨#000033¨»(«/mo»«mi mathvariant=¨normal¨ mathcolor=¨#000033¨»x«/mi»«mo mathcolor=¨#000033¨»-«/mo»«mn mathcolor=¨#000033¨»1«/mn»«mo mathcolor=¨#000033¨»)«/mo»«mo mathcolor=¨#000033¨»(«/mo»«mi mathvariant=¨normal¨ mathcolor=¨#000033¨»x«/mi»«mo mathcolor=¨#000033¨»-«/mo»«mn mathcolor=¨#000033¨»2«/mn»«mo mathcolor=¨#000033¨»)«/mo»«mo mathcolor=¨#000033¨»(«/mo»«mi mathvariant=¨normal¨ mathcolor=¨#000033¨»x«/mi»«mo mathcolor=¨#000033¨»-«/mo»«mn mathcolor=¨#000033¨»4«/mn»«mo mathcolor=¨#000033¨»)«/mo»«/mrow»«/mstyle»«/math»



]]> 0.0000000 0.0000000 0 1.2.4.41Q FactoritzaRuffini G3 Factoritza el polinomi «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: 4(x+2)(x-1)^2

]]>  

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>)</mo><mo>*</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math 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open="|"><mi>a2</mi></mfenced></mrow><mtable><mtr><mtd><mi>r1</mi><mo>=</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>a3</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>r1</mi><mo>=</mo><mi>a3</mi></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>a2</mi></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>r2</mi><mo>=</mo><mi>r3</mi></mrow><mrow><mi>M</mi><mo>=</mo><mo>&quot;</mo><mi>conté</mi><mo> </mo><mi>un</mi><mo> </mo><mi>quadrat</mi><mo> </mo><mi>perfecte</mi><mo>&quot;</mo></mrow><apply><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>,</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>14</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>150</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mn>5</mn></mrow></mfenced><mn>2</mn></msup><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>20</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>50</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>té</ms><mo> </mo><ms>un</ms><mo> </mo><ms>quadrat</ms><mo> </mo><ms>perfecte</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que es tracta d'un polinomi amb terme independent i grau superior a 2, es comença pel mètode de Ruffini.

El primer divisor és #t1, i el quocient #P1.

]]> Per factoritzar #P1, #M.

]]> 1.2.4.42Q FactoritzaRuffini G4 Factoritza el polinomi «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: 4*(x+2)*(x-1)^2*(x-4)

]]>  

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a0</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a3</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a0</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>P</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mi>mínim</mi><mo>(</mo><mfenced close="|" open="|"><mi>a0</mi></mfenced><mo>,</mo><mfenced close="|" open="|"><mi>a1</mi></mfenced><mo>,</mo><mfenced close="|" open="|"><mi>a2</mi></mfenced><mo>,</mo><mfenced close="|" open="|"><mi>a3</mi></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>m1</mi><mo>=</mo><mfenced close="|" open="|"><mi>a0</mi></mfenced></mrow><mtable><mtr><mtd><mi>r0</mi><mo>=</mo><mi>a0</mi></mtd></mtr><mtr><mtd><mi>r1</mi><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>a3</mi></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>m1</mi><mo>=</mo><mfenced close="|" open="|"><mi>a1</mi></mfenced></mrow><mtable><mtr><mtd><mi>r0</mi><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>r1</mi><mo>=</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mi>a3</mi></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>a0</mi></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>m1</mi><mo>=</mo><mfenced close="|" open="|"><mi>a2</mi></mfenced></mrow><mtable><mtr><mtd><mi>r0</mi><mo>=</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>r1</mi><mo>=</mo><mi>a3</mi></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mi>a0</mi></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>a1</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>r0</mi><mo>=</mo><mi>a3</mi></mtd></mtr><mtr><mtd><mi>r1</mi><mo>=</mo><mi>a0</mi></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>a2</mi></mtd></mtr></mtable></apply></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>mínim</mi><mfenced><mrow><mfenced close="|" open="|"><mi>r1</mi></mfenced><mo>,</mo><mfenced close="|" open="|"><mi>r2</mi></mfenced><mo>,</mo><mfenced close="|" open="|"><mi>r3</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>s</mi><mo>=</mo><mfenced close="|" open="|"><mi>r1</mi></mfenced></mrow><mtable><mtr><mtd><mi>s1</mi><mo>=</mo><mi>r1</mi></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mi>r2</mi></mtd></mtr><mtr><mtd><mi>s3</mi><mo>=</mo><mi>r3</mi></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>s</mi><mo>=</mo><mfenced close="|" open="|"><mi>r2</mi></mfenced></mrow><mtable><mtr><mtd><mi>s1</mi><mo>=</mo><mi>r2</mi></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mi>r3</mi></mtd></mtr><mtr><mtd><mi>s3</mi><mo>=</mo><mi>r1</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>s1</mi><mo>=</mo><mi>r3</mi></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mi>r1</mi></mtd></mtr><mtr><mtd><mi>s3</mi><mo>=</mo><mi>r2</mi></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P2</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P3</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s3</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>r0</mi><mo>=</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>M1</mi><mo>=</mo><mo>&quot;</mo><mi>sense</mi><mo> </mo><mi>terme</mi><mo> </mo><mi>independent</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>M2</mi><mo>=</mo><mo>&quot;</mo><mi>Traiem</mi><mo> </mo><mi>x</mi><mo> </mo><mi>en</mi><mo> </mo><mi>factor</mi><mo>,</mo><mo> </mo><mi>i</mi><mo> </mo><mi>apliquem</mi><mo> </mo><mi>el</mi><mo> </mo><mi>mètode</mi><mo> </mo><mi>de</mi><mo> </mo><mi>Ruffini</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>M3</mi><mo>=</mo><mo>&quot;</mo><mi>El</mi><mo> </mo><mi>primer</mi><mo> </mo><mi>divisor</mi><mo> </mo><mi>és</mi><mo>&quot;</mo><mo> </mo></mtd></mtr><mtr><mtd><mi>M4</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>s1</mi></mtd></mtr><mtr><mtd><mi>M5</mi><mo>=</mo><mo>&quot;</mo><mi>Les</mi><mo> </mo><mi>arrels</mi><mo> </mo><mi>del</mi><mo> </mo><mi>quocient</mi><mo> </mo><mi>de</mi><mo> </mo><mi>segon</mi><mo> </mo><mi>grau</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>M6</mi><mo>=</mo><mi>P2</mi></mtd></mtr><mtr><mtd><mi>M7</mi><mo>=</mo><mo>&quot;</mo><mi>són</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>M8</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>s2</mi><mo>,</mo><mi>s3</mi></mtd></mtr></mtable></mfenced></mtd></mtr></mtable><mtable><mtr><mtd><mi>M1</mi><mo>=</mo><mo>&quot;</mo><mi>que</mi><mo> </mo><mi>té</mi><mo> </mo><mi>terme</mi><mo> </mo><mi>independent</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>M2</mi><mo>=</mo><mo>&quot;</mo><mi>Apliquem</mi><mo> </mo><mi>el</mi><mo> </mo><mi>mètode</mi><mo> </mo><mi>de</mi><mo> </mo><mi>Ruffini</mi><mo>.</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>M3</mi><mo>=</mo><mo>&quot;</mo><mi>El</mi><mo> </mo><mi>primer</mi><mo> </mo><mi>divisor</mi><mo> </mo><mi>és</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>M4</mi><mo>=</mo><mo> </mo><mi>x</mi><mo>-</mo><mi>r0</mi></mtd></mtr><mtr><mtd><mi>M5</mi><mo>=</mo><mo>&quot;</mo><mi>Tornem</mi><mo> </mo><mi>a</mi><mo> </mo><mi>aplicar</mi><mo> </mo><mi>el</mi><mo> </mo><mi>mètode</mi><mo> </mo><mi>de</mi><mo> </mo><mi>Ruffini</mi><mo> </mo><mi>a</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>M6</mi><mo>=</mo><mi>P3</mi></mtd></mtr><mtr><mtd><mi>M7</mi><mo>=</mo><mo>&quot;</mo><mi>El</mi><mo> </mo><mi>segon</mi><mo> </mo><mi>divisor</mi><mo> </mo><mi>és</mi><mo> </mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>M8</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>s1</mi></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a0</mi><mo>,</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>a3</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r0</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>12</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>16</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>48</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>sense</ms><mo> </mo><ms>terme</ms><mo> </mo><ms>independent</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Traiem</ms><mo> </mo><ms>x</ms><mo> </mo><ms>en</ms><mo> </mo><ms>factor,</ms><mo> </mo><ms>i</ms><mo> </mo><ms>apliquem</ms><mo> </mo><ms>el</ms><mo> </mo><ms>mètode</ms><mo> </mo><ms>de</ms><mo> </mo><ms>Ruffini</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>El</ms><mo> </mo><ms>primer</ms><mo> </mo><ms>divisor</ms><mo> </mo><ms>és</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Les</ms><mo> </mo><ms>arrels</ms><mo> </mo><ms>del</ms><mo> </mo><ms>quocient</ms><mo> </mo><ms>de</ms><mo> </mo><ms>segon</ms><mo> </mo><ms>grau</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M6</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>24</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M7</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>són</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M8</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>3</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> #P és un polinomi de grau 4, #M1.

#M2 #M3 #M4

]]> #M5 #M6 #M7.   #M8

]]> 1.2.4.43Q FactoritzaRuffini G4 (G2 sense solució) Factoritza el polinomi P(x) = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo»§#160;«/mo»«/mrow»«/mstyle»«/math»

Format de la resposta: (x+2)·(x-1)·(2x2+4x+9)

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></mtd></mtr></mtable><mrow><mi>d</mi><mo>&lt;</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>r1</mi><mo>=</mo><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>r1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>r2</mi><mo>)</mo><mo>*</mo><mi>Q</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>P</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mfenced close="|" open="|"><mi>r1</mi></mfenced><mo>&lt;</mo><mfenced close="|" open="|"><mi>r2</mi></mfenced></mrow><mtable><mtr><mtd><mi>f1</mi><mo>=</mo><mi>r1</mi></mtd></mtr><mtr><mtd><mi>f2</mi><mo>=</mo><mi>r2</mi></mtd></mtr><mtr><mtd><mi>Q1</mi><mo>=</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>r2</mi><mo>)</mo><mo>*</mo><mi>Q</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>f1</mi><mo>=</mo><mi>r2</mi></mtd></mtr><mtr><mtd><mi>f2</mi><mo>=</mo><mi>r1</mi></mtd></mtr><mtr><mtd><mi>Q1</mi><mo>=</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>r1</mi><mo>)</mo><mo>*</mo><mi>Q</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>f1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>f2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c0</mi><mo>=</mo><msub><mi>P</mi><mn>0</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><msub><mi>P</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><msub><mi>P</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><msub><mi>P</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c4</mi><mo>=</mo><msub><mi>P</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g3</mi><mo>=</mo><msub><mi>Q1</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g2</mi><mo>=</mo><msub><mi>Q1</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g1</mi><mo>=</mo><msub><mi>Q1</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g0</mi><mo>=</mo><msub><mi>Q1</mi><mn>0</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>divisors</mi><mo>(</mo><mi>c0</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mi>divisors</mi><mo>(</mo><mi>g0</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h3</mi><mo>=</mo><mi>f1</mi><mo>*</mo><mi>g3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h2</mi><mo>=</mo><mi>f1</mi><mo>*</mo><mi>g2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h1</mi><mo>=</mo><mi>f1</mi><mo>*</mo><mi>g1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h0</mi><mo>=</mo><mi>f1</mi><mo>*</mo><mi>g0</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>r1</mi><mo>,</mo><mi>r2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>f1</mi><mo>,</mo><mi>f2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>22</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>c0</mi><mo>,</mo><mi>c1</mi><mo>,</mo><mi>c2</mi><mo>,</mo><mi>c3</mi><mo>,</mo><mi>c4</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>15</mn><mo>,</mo><mo>-</mo><mn>22</mn><mo>,</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>15</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>15</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>15</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que el polinomi és de grau superior a 2 i té terme independent, #c0, cal emprar el mètode de Ruffini amb tots els divisors de #c0 que són: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#177;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»t«/mi»«/math».

El primer divisor és #t1:

  #c4 #c3 #c2 #c1 #c0
#f1          
           
]]> El resultat de la primera divisió per  #t1 ens dona de quocient #Q1. Com que el grau és superior a 2, i té terme independent, #g2, cal emprar el mètode de Ruffini amb  tots els divisors de #g0, que són «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#177;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»u«/mi»«/math».

El segon divisor és #t2:

  #c4 #c3 #c2 #c1 #c0
#f1    #h3 #h2  #h1   #h0
   #g3 #g2 #g1  #g0   0
#f2          

Ara cal resoldre, si es pot, l'equació de 2n grau.

]]> 1.2.4.44Q FactoritzaRuffini G5 Factoritza el polinomi P(x) = #P

Format de la resposta: 4*(x+2)*(x-1)^2*(x-4)

]]>  

]]> 1.0000000 0.5000000 0 0 #r_1]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_0</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mfenced><mrow><mfenced><mrow><mi>a_4</mi><mo>*</mo><mi>a_3</mi><mo>*</mo><mi>a_3</mi><mo>*</mo><mi>a_2</mi><mo>*</mo><mi>a_1</mi><mo>*</mo><mi>a_0</mi></mrow></mfenced><mo>&lt;</mo><mn>41</mn></mrow></mfenced></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>a_4</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_3</mi><msup><mo>)</mo><mn>2</mn></msup><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_0</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>a_4</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_3</mi><msup><mo>)</mo><mn>2</mn></msup><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_0</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>mínim</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>a_3</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_1</mi><mo>,</mo><mi>a_0</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>d1</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_0</mi><mo>,</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>5</mn></msup><mo>-</mo><mn>13</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>59</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>95</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>24</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>144</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced><mn>2</mn></msup><mo>*</mo><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfenced><mn>2</mn></msup><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> És de grau superior a 2 i té terme independent, cal emprar el mètode de Ruffini.

El primer divisor és #d2

]]> 1.2.4.45 AssociaPolFactorització Associa cada polinomi amb la seva descomposició factorial.

]]> 1.0000000 0.5000000 0 true #poli1

]]> #sol1 #poli2

]]> #sol2 #poli3

]]> #sol3 <question><wirisCasSession>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;apply&gt;&lt;csymbol definitionURL=&quot;http://www.wiris.com/XML/csymbol&quot;&gt;repeat&lt;/csymbol&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;≠&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;∧&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;≠&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;∧&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;≠&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/apply&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;x1&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;x2&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;x3&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;poli1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;x1&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;x2&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;x3&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;sol1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;factoritza&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;poli1&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;y1&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;y2&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;y3&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;poli2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;y1&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;y2&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;y3&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;sol2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;factoritza&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;poli2&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;z1&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;z2&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;z3&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;poli3&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;z1&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;z2&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;z3&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math 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xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;sol1&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><localData><data name="cas">false</data></localData></question> 1.2.4.50DT FACTORITZA POLINOMI QUALSEVOL

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0.0000000 0.0000000 0 1.2.4.51Q Factoritza G3 DDQ Factoritza el polinomi P(x) = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: 4(x+2)(x-2)

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P2</mi><mo>=</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>P</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>a1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>18</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer s'aplica el mètode de Ruffini, 

En el quocient, es pot treure #a en factor comú per posar en evidència la diferència de quadrats: 

#P1 = #a · (#P2)

]]> 1.2.4.52Q Factoritza G3 QPerfecte Factoritza el polinomi P(x) = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: 4(x+2)(x-2)

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P2</mi><mo>=</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>P</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>a1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>27</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>45</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>75</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>30</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>75</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>25</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mn>5</mn></mrow></mfenced><mn>2</mn></msup><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer s'aplica el mètode de Ruffini, 

En el quocient, es pot treure #a en factor comú per posar en evidència el quadrat d'una suma: 

#P1 = #a · (#P2)

]]> 1.2.4.53Q Factoritza G6 QPerf Factoritza el polinomi P(x) = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: 4(x+2)(x-1)2(x-4)

]]>  

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_0</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>8</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mfenced><mrow><mfenced><mrow><mi>a_4</mi><mo>*</mo><mi>a_3</mi><mo>*</mo><mi>a_3</mi><mo>*</mo><mi>a_2</mi><mo>*</mo><mi>a_1</mi><mo>*</mo><mi>a_0</mi></mrow></mfenced><mo>&lt;</mo><mn>41</mn></mrow></mfenced></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>a_4</mi><mo>*</mo><msup><mi>x</mi><mi>n</mi></msup><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_3</mi><msup><mo>)</mo><mn>2</mn></msup><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_1</mi><msup><mo>)</mo><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>a_4</mi><mo>*</mo><msup><mi>x</mi><mi>n</mi></msup><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_3</mi><msup><mo>)</mo><mn>2</mn></msup><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_1</mi><msup><mo>)</mo><mn>2</mn></msup><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_0</mi><mo>,</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>9</mn></msup><mo>+</mo><mn>57</mn><mo>*</mo><msup><mi>x</mi><mn>8</mn></msup><mo>-</mo><mn>417</mn><mo>*</mo><msup><mi>x</mi><mn>7</mn></msup><mo>+</mo><mn>1443</mn><mo>*</mo><msup><mi>x</mi><mn>6</mn></msup><mo>-</mo><mn>2280</mn><mo>*</mo><msup><mi>x</mi><mn>5</mn></msup><mo>+</mo><mn>1200</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>*</mo><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mn>5</mn></mrow></mfenced><mn>2</mn></msup><mo>*</mo><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced><mn>2</mn></msup><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Es comença traient x en factor ja que el polinomi no té terme independent.

Després fins a grau 2, s'aplica el mètode de Ruffini.

L'últim quocient de grau 2 és una diferència de quadrats.

]]> 1.2.4.54Q Factoritza G6 DDQ Factoritza el polinomi P(x) = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: 4(x+2)(x-1)2(x-4)

]]>  

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_0</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>8</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mfenced><mrow><mfenced><mrow><mi>a_4</mi><mo>*</mo><mi>a_3</mi><mo>*</mo><mi>a_3</mi><mo>*</mo><mi>a_2</mi><mo>*</mo><mi>a_1</mi><mo>*</mo><mi>a_0</mi></mrow></mfenced><mo>&lt;</mo><mn>41</mn></mrow></mfenced></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>a_4</mi><mo>*</mo><msup><mi>x</mi><mi>n</mi></msup><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_3</mi><msup><mo>)</mo><mn>2</mn></msup><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a_1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>a_4</mi><mo>*</mo><msup><mi>x</mi><mi>n</mi></msup><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_3</mi><msup><mo>)</mo><mn>2</mn></msup><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a_1</mi><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_0</mi><mo>,</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>8</mn></msup><mo>-</mo><mn>12</mn><mo>*</mo><msup><mi>x</mi><mn>7</mn></msup><mo>+</mo><mn>132</mn><mo>*</mo><msup><mi>x</mi><mn>6</mn></msup><mo>+</mo><mn>582</mn><mo>*</mo><msup><mi>x</mi><mn>5</mn></msup><mo>+</mo><mn>735</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>294</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>7</mn></mrow></mfenced><mo>*</mo><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>7</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Es comença traient x en factor ja que el polinomi no té terme independent.

Després fins a grau 2, s'aplica el mètode de Ruffini.

L'últim quocient de grau 2 és una diferència de quadrats.

]]> 1.2.4.55Q FactoritzaArrels G4 Biquadrada Factoritza i calcula les arrels del polinomi P(x) = #P

Format de la resposta:

a) 4(x+2)(x-2)

b) {-1,1,2,2} Posa-les totes, si n'hi ha de dobles, escriu-les dos cops

]]> 1.0000000 0.5000000 0 0 a)Factorització=#sol1b)Arrels=#sol2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>P</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>arrels</mi><mo>(</mo><mi>P</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>52</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>50</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>5</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>5</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mi>F</mi><mi>a</mi><mi>c</mi><mi>t</mi><mi>o</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi>z</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>&#xF3;</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mi>A</mi><mi>r</mi><mi>r</mi><mi mathvariant="normal">e</mi><mi>l</mi><mi>s</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> L'equació corresponent és una equació biquadrada.

Es fa el canvi de variable t = x2 i t2 = x4, i es resol per trobar t. 

El pas següent és trobar x desfent el canvi de variable amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#177;«/mo»«msqrt mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨»t«/mi»«/msqrt»«/mrow»«/mstyle»«/math»

 

]]> 1.2.4.60MADT RUFFINI ARRELS FRACCIONÀRIES  

Mètode de Ruffini amb arrels fraccionàries

Si un polinomi  té terme independent i grau superior a 2, es va dividint per (x-a)  fins al grau 2 pel mètode de Ruffini. Si el coeficient del terme de grau més alt és diferent de 1, pot ser que a sigui una fracció.

DIVISORS FRACCIONARIS: Són totes les fraccions que es poden formar amb al numerador els divisors del terme independent  i al denominador els divisors del coeficient del terme de grau més alt .

Amb 6x5 - 3x4  + 7x3 +2x+15 cal provar ±1/2,±1/3,±1/5,±3/2...



]]> 0.0000000 0.0000000 0 1.2.4.61Q FactoritzaRuffiniArrelsFracG3 Factoritza el polinomi «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: 4(x+2)(x-1)^2

]]>  

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>5</mn></mtd></mtr></mtable></mfenced><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>P</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mfrac><mi>a1</mi><mi>a</mi></mfrac><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a3</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>a1</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><msub><mi>P</mi><mn>0</mn></msub><mo>∈</mo><integers/></mrow></mfenced><mo>∧</mo><mfenced><mrow><msub><mi>P</mi><mn>1</mn></msub><mo>∈</mo><integers/></mrow></mfenced><mo>∧</mo><mfenced><mrow><msub><mi>P</mi><mn>2</mn></msub><mo>∈</mo><integers/></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>P</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>divisors</mi><mo>(</mo><msub><mi>P</mi><mn>0</mn></msub><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>divisors</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>a3</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>25</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>37</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>280</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>0</mn></msub></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>280</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>1</mn></msub></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>37</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>2</mn></msub></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>+</mo><mn>7</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>8</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>,</mo><mi>d1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>,</mo><mn>40</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>14</mn><mo>,</mo><mn>28</mn><mo>,</mo><mn>56</mn><mo>,</mo><mn>35</mn><mo>,</mo><mn>70</mn><mo>,</mo><mn>140</mn><mo>,</mo><mn>280</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">3</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Es comença amb el mètode de Ruffini.

Com que el coeficient del grau més alt, no és 1, es proven les fraccions formades:

  • al numerador pels divisors del terme independent «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»n«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/mrow»«/mstyle»«/math»
  • al denominador pels divisors del terme de grau més alt «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»d«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/mrow»«/mstyle»«/math» excepte l'1, perquè ja no seria una fracció!
]]> 1.2.4.70DT ARRELS D'UN POLINOMI  

Arrel d'un polinomi

a és arrel d'un polinomi P(x) si, i només si, P(a) = 0. 

Per determinar les arrels d'un polinomi  de grau superior a 2 es factoritza, si el grau és inferior o igual a 2, es resol l'equació polinòmica següent.
Exemple:
-2x4 + 10x3 -12x2 =(-2)· x2 · (x-2)(x-3) 

i les arrels són 0 (doble), 2 i 3.

Es diu que a és arrel múltiple d'un polinomi si en la factorització, el factor (x-a) apareix més d'un cop. k és la multiplicitat de l'arrel a si el factor corresponent és (x-a)k



]]> 0.0000000 0.0000000 0 1.2.4.71VF DeterminarSiUnNombreÉsArrel x = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«/mrow»«/mstyle»«/math»és una arrel del polinomi P(x) = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»poli«/mi»«/mrow»«/mstyle»«/math»?I per tant, el polinomi és divisible per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«/mrow»«/mstyle»«/math» ?

]]> 1.0000000 1.0000000 0 Vertader Fals <question><wirisCasSession>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;x1&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;x2&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;x3&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;poli&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;·&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;x1&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;·&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;x2&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;·&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;x3&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;sol&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;x1&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mo&gt;∨&lt;/mo&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;x2&lt;/mi&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mo&gt;∨&lt;/mo&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;x3&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;?&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;sol&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;fals&lt;/mi&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><localData><data name="cas">false</data></localData></question> 1.2.4.72Q Trobar k per tal que a sigui arrel Calcula el valor del coeficient k perquè «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«/mrow»«/mstyle»«/math» sigui una arrel del polinomi P(x) = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»poli«/mi»«/mrow»«/mstyle»«/math».]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;apply&gt;&lt;csymbol definitionURL=&quot;http://www.wiris.com/XML/csymbol&quot;&gt;repeat&lt;/csymbol&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;≠&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/apply&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;poli&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;kx&lt;/mi&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;sol&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;msup&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/msup&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;poli&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;kx&lt;/mi&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mfrac&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;sol&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;92&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml"> #sol </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> 1.2.4.73Q Arrels G3 Quines són les arrels del polinomi P(x) = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»P«/mi»«/mrow»«/mstyle»«/math»?

Format de la resposta: {-2,0,1,1}

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>)</mo><mo>*</mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mi>mínim</mi><mo>(</mo><mfenced close="|" open="|"><mi>a1</mi></mfenced><mo>,</mo><mfenced close="|" open="|"><mi>a2</mi></mfenced><mo>,</mo><mfenced close="|" open="|"><mi>a3</mi></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>m1</mi><mo>=</mo><mfenced close="|" open="|"><mi>a1</mi></mfenced></mrow><mtable><mtr><mtd><mi>r1</mi><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>a3</mi></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>m1</mi><mo>=</mo><mfenced close="|" open="|"><mi>a2</mi></mfenced></mrow><mtable><mtr><mtd><mi>r1</mi><mo>=</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>a3</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>r1</mi><mo>=</mo><mi>a3</mi></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>a2</mi></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>r2</mi><mo>=</mo><mi>r3</mi></mrow><mrow><mi>M</mi><mo>=</mo><mo>&quot;</mo><mi>conté</mi><mo> </mo><mi>un</mi><mo> </mo><mi>quadrat</mi><mo> </mo><mi>perfecte</mi><mo>&quot;</mo></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>r2</mi><mo>=</mo><mo>-</mo><mi>r3</mi></mrow><mrow><mi>M</mi><mo>=</mo><mo>&quot;</mo><mi>conté</mi><mo> </mo><mi>una</mi><mo> </mo><mi>diferència</mi><mo> </mo><mi>de</mi><mo> </mo><mi>quadrats</mi><mo>&quot;</mo></mrow><mrow><mi>M</mi><mo>=</mo><mo>&quot;</mo><mi>es</mi><mo> </mo><mi>calcula</mi><mo> </mo><mi>el</mi><mo> </mo><mi>discriminant</mi><mo>&quot;</mo></mrow></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>r1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi><mo>=</mo><mi>quocient</mi><mo>(</mo><mi>P</mi><mo>,</mo><mi>t1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>{</mo><mi>r1</mi><mo>,</mo><mi>r2</mi><mo>,</mo><mi>r3</mi><mo>}</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>a3</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>18</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>36</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>conté</ms><mo> </mo><ms>una</ms><mo> </mo><ms>diferència</ms><mo> </mo><ms>de</ms><mo> </mo><ms>quadrats</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">2</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que es tracta d'un polinomi amb terme independent i grau superior a 2, es comença pel mètode de Ruffini.

El primer divisor és #t1, i el quocient #P1.

 

Per factoritzar #P1, #M.

]]> 1.2.4.74Q Arrels G4 Troba les arrels, si s'escau del polinomi P(x) = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«/mrow»«/mstyle»«/math»


Format de la resposta: {-1,2,2,4}

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]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a0</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a3</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a0</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>{</mo><mi>a3</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>a1</mi><mo>,</mo><mi>a0</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mi>mínim</mi><mo>(</mo><mfenced close="|" open="|"><mi>a0</mi></mfenced><mo>,</mo><mfenced close="|" open="|"><mi>a1</mi></mfenced><mo>,</mo><mfenced close="|" open="|"><mi>a2</mi></mfenced><mo>,</mo><mfenced close="|" open="|"><mi>a3</mi></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>m1</mi><mo>=</mo><mfenced close="|" open="|"><mi>a0</mi></mfenced></mrow><mtable><mtr><mtd><mi>r0</mi><mo>=</mo><mi>a0</mi></mtd></mtr><mtr><mtd><mi>r1</mi><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>a3</mi></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>m1</mi><mo>=</mo><mfenced close="|" open="|"><mi>a1</mi></mfenced></mrow><mtable><mtr><mtd><mi>r0</mi><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>r1</mi><mo>=</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mi>a3</mi></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>a0</mi></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>m1</mi><mo>=</mo><mfenced close="|" open="|"><mi>a2</mi></mfenced></mrow><mtable><mtr><mtd><mi>r0</mi><mo>=</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>r1</mi><mo>=</mo><mi>a3</mi></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mi>a0</mi></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>a1</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>r0</mi><mo>=</mo><mi>a3</mi></mtd></mtr><mtr><mtd><mi>r1</mi><mo>=</mo><mi>a0</mi></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>a2</mi></mtd></mtr></mtable></apply></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>mínim</mi><mfenced><mrow><mfenced close="|" open="|"><mi>r1</mi></mfenced><mo>,</mo><mfenced close="|" open="|"><mi>r2</mi></mfenced><mo>,</mo><mfenced close="|" open="|"><mi>r3</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>s</mi><mo>=</mo><mfenced close="|" open="|"><mi>r1</mi></mfenced></mrow><mtable><mtr><mtd><mi>s1</mi><mo>=</mo><mi>r1</mi></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mi>r2</mi></mtd></mtr><mtr><mtd><mi>s3</mi><mo>=</mo><mi>r3</mi></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>s</mi><mo>=</mo><mfenced close="|" open="|"><mi>r2</mi></mfenced></mrow><mtable><mtr><mtd><mi>s1</mi><mo>=</mo><mi>r2</mi></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mi>r3</mi></mtd></mtr><mtr><mtd><mi>s3</mi><mo>=</mo><mi>r1</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>s1</mi><mo>=</mo><mi>r3</mi></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mi>r1</mi></mtd></mtr><mtr><mtd><mi>s3</mi><mo>=</mo><mi>r2</mi></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P2</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P3</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s3</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>r0</mi><mo>=</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>M1</mi><mo>=</mo><mo>&quot;</mo><mi>sense</mi><mo> </mo><mi>terme</mi><mo> </mo><mi>independent</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>M2</mi><mo>=</mo><mo>&quot;</mo><mi>Traiem</mi><mo> </mo><mi>x</mi><mo> </mo><mi>en</mi><mo> </mo><mi>factor</mi><mo>,</mo><mo> </mo><mi>i</mi><mo> </mo><mi>apliquem</mi><mo> </mo><mi>el</mi><mo> </mo><mi>mètode</mi><mo> </mo><mi>de</mi><mo> </mo><mi>Ruffini</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>M3</mi><mo>=</mo><mo>&quot;</mo><mi>El</mi><mo> </mo><mi>primer</mi><mo> </mo><mi>divisor</mi><mo> </mo><mi>és</mi><mo>&quot;</mo><mo> </mo></mtd></mtr><mtr><mtd><mi>M4</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>s1</mi></mtd></mtr><mtr><mtd><mi>M5</mi><mo>=</mo><mo>&quot;</mo><mi>Les</mi><mo> </mo><mi>arrels</mi><mo> </mo><mi>del</mi><mo> </mo><mi>quocient</mi><mo> </mo><mi>de</mi><mo> </mo><mi>segon</mi><mo> </mo><mi>grau</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>M6</mi><mo>=</mo><mi>P2</mi></mtd></mtr><mtr><mtd><mi>M7</mi><mo>=</mo><mo>&quot;</mo><mi>són</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>M8</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>s2</mi><mo>,</mo><mi>s3</mi></mtd></mtr></mtable></mfenced></mtd></mtr></mtable><mtable><mtr><mtd><mi>M1</mi><mo>=</mo><mo>&quot;</mo><mi>que</mi><mo> </mo><mi>té</mi><mo> </mo><mi>terme</mi><mo> </mo><mi>independent</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>M2</mi><mo>=</mo><mo>&quot;</mo><mi>Apliquem</mi><mo> </mo><mi>el</mi><mo> </mo><mi>mètode</mi><mo> </mo><mi>de</mi><mo> </mo><mi>Ruffini</mi><mo>.</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>M3</mi><mo>=</mo><mo>&quot;</mo><mi>El</mi><mo> </mo><mi>primer</mi><mo> </mo><mi>divisor</mi><mo> </mo><mi>és</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>M4</mi><mo>=</mo><mo> </mo><mi>x</mi><mo>-</mo><mi>r0</mi></mtd></mtr><mtr><mtd><mi>M5</mi><mo>=</mo><mo>&quot;</mo><mi>Tornem</mi><mo> </mo><mi>a</mi><mo> </mo><mi>aplicar</mi><mo> </mo><mi>el</mi><mo> </mo><mi>mètode</mi><mo> </mo><mi>de</mi><mo> </mo><mi>Ruffini</mi><mo> </mo><mi>a</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>M6</mi><mo>=</mo><mi>P3</mi></mtd></mtr><mtr><mtd><mi>M7</mi><mo>=</mo><mo>&quot;</mo><mi>El</mi><mo> </mo><mi>segon</mi><mo> </mo><mi>divisor</mi><mo> </mo><mi>és</mi><mo> </mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>M8</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>s1</mi></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a0</mi><mo>,</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>a3</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r0</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>12</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>16</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>48</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>sense</ms><mo> </mo><ms>terme</ms><mo> </mo><ms>independent</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Traiem</ms><mo> </mo><ms>x</ms><mo> </mo><ms>en</ms><mo> </mo><ms>factor,</ms><mo> </mo><ms>i</ms><mo> </mo><ms>apliquem</ms><mo> </mo><ms>el</ms><mo> </mo><ms>mètode</ms><mo> </mo><ms>de</ms><mo> </mo><ms>Ruffini</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>El</ms><mo> </mo><ms>primer</ms><mo> </mo><ms>divisor</ms><mo> </mo><ms>és</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Les</ms><mo> </mo><ms>arrels</ms><mo> </mo><ms>del</ms><mo> </mo><ms>quocient</ms><mo> </mo><ms>de</ms><mo> </mo><ms>segon</ms><mo> </mo><ms>grau</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M6</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>24</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M7</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>són</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M8</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>3</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Es factoritza el polinomi per trobar les seves arrels.

#P és un polinomi de grau 4, #M1.

#M2 #M3 #M4

]]> #M5 #M6 #M7.   #M8

]]> 1.2.4.75Q Arrels G4_2 Troba les arrels, si s'escau, del polinomi P(x) = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: {-1,2,2,4} repeteix-la si n'hi ha cap de doble

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]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a0</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a3</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a0</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>{</mo><mi>a3</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>a1</mi><mo>,</mo><mi>a0</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mi>mínim</mi><mo>(</mo><mfenced close="|" open="|"><mi>a0</mi></mfenced><mo>,</mo><mfenced close="|" open="|"><mi>a1</mi></mfenced><mo>,</mo><mfenced close="|" open="|"><mi>a2</mi></mfenced><mo>,</mo><mfenced close="|" open="|"><mi>a3</mi></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>m1</mi><mo>=</mo><mfenced close="|" open="|"><mi>a0</mi></mfenced></mrow><mtable><mtr><mtd><mi>r0</mi><mo>=</mo><mi>a0</mi></mtd></mtr><mtr><mtd><mi>r1</mi><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>a3</mi></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>m1</mi><mo>=</mo><mfenced close="|" open="|"><mi>a1</mi></mfenced></mrow><mtable><mtr><mtd><mi>r0</mi><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>r1</mi><mo>=</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mi>a3</mi></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>a0</mi></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>m1</mi><mo>=</mo><mfenced close="|" open="|"><mi>a2</mi></mfenced></mrow><mtable><mtr><mtd><mi>r0</mi><mo>=</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>r1</mi><mo>=</mo><mi>a3</mi></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mi>a0</mi></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>a1</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>r0</mi><mo>=</mo><mi>a3</mi></mtd></mtr><mtr><mtd><mi>r1</mi><mo>=</mo><mi>a0</mi></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>a2</mi></mtd></mtr></mtable></apply></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>mínim</mi><mfenced><mrow><mfenced close="|" open="|"><mi>r1</mi></mfenced><mo>,</mo><mfenced close="|" open="|"><mi>r2</mi></mfenced><mo>,</mo><mfenced close="|" open="|"><mi>r3</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>r0</mi><mo>=</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>M1</mi><mo>=</mo><mo>&quot;</mo><mi>sense</mi><mo> </mo><mi>terme</mi><mo> </mo><mi>independent</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>M2</mi><mo>=</mo><mo>&quot;</mo><mi>Traiem</mi><mo> </mo><mi>x</mi><mo> </mo><mi>en</mi><mo> </mo><mi>factor</mi><mo>,</mo><mo> </mo><mi>i</mi><mo> </mo><mi>apliquem</mi><mo> </mo><mi>el</mi><mo> </mo><mi>mètode</mi><mo> </mo><mi>de</mi><mo> </mo><mi>Ruffini</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>M3</mi><mo>=</mo><mo>&quot;</mo><mi>El</mi><mo> </mo><mi>primer</mi><mo> </mo><mi>divisor</mi><mo> </mo><mi>és</mi><mo>&quot;</mo><mo> </mo></mtd></mtr><mtr><mtd><mi>M4</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>s1</mi></mtd></mtr><mtr><mtd><mi>M5</mi><mo>=</mo><mo>&quot;</mo><mi>Les</mi><mo> </mo><mi>arrels</mi><mo> </mo><mi>del</mi><mo> </mo><mi>quocient</mi><mo> </mo><mi>de</mi><mo> </mo><mi>segon</mi><mo> </mo><mi>grau</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>M6</mi><mo>=</mo><mi>P2</mi></mtd></mtr><mtr><mtd><mi>M7</mi><mo>=</mo><mo>&quot;</mo><mi>són</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>M8</mi><mo>=</mo><mfenced 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xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a0</mi><mo>,</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>a3</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r0</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>12</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>16</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>48</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>sense</ms><mo> </mo><ms>terme</ms><mo> </mo><ms>independent</ms></math></output></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><ms>Les</ms><mo> </mo><ms>arrels</ms><mo> </mo><ms>del</ms><mo> </mo><ms>quocient</ms><mo> </mo><ms>de</ms><mo> </mo><ms>segon</ms><mo> </mo><ms>grau</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M6</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>24</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M7</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>són</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M8</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>3</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">8</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Es factoritza el polinomi per trobar les seves arrels.

#P és un polinomi de grau 4, #M1.

#M2 #M3 #M4

]]> #M5 #M6 #M7.   #M8

Ara ja es poden trobar les arrels del polinomi de 2n grau que queda, trobant les solucions de l'equació de segon grau corresponent:

]]> 1.2.4.76Q Arrels G5 Troba les arrels del polinomi P(x) = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: {-2,-1, 0, 1,2,3} Si hi ha una arrel múltiple s'ha de repetir!

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]]> 1.0000000 0.5000000 0 0 #r_1]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_0</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>a_4</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_3</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a_3</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_1</mi><msup><mo>)</mo><mn>3</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mi>ordena</mi><mo>(</mo><mo>{</mo><mi>a_1</mi><mo>,</mo><mi>a_1</mi><mo>,</mo><mi>a_1</mi><mo>,</mo><mo>-</mo><mi>a_3</mi><mo>,</mo><mi>a_3</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mi>mínim</mi><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_3</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_0</mi><mo>,</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>5</mn></msup><mo>-</mo><mn>12</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>16</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>32</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>96</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>64</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Cal començar amb el mètode de Ruffini.

]]> 1.2.4.77Q Arrels G5 Sense TI Troba les arrels del polinomi P(x) = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: {-2,-1, 0, 1,2,3} Si hi ha una arrel múltiple s'ha de repetir!

]]>  

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>a1</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a3</mi><msup><mo>)</mo><mn>2</mn></msup><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>{</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>,</mo><mo>-</mo><mi>a3</mi><mo>,</mo><mi>a3</mi><mo>,</mo><mi>a3</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi><mo>=</mo><mfrac><mi>P</mi><msup><mi>x</mi><mn>2</mn></msup></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a3</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>5</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>0</mn><mo>,</mo><mn>0</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">8</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Cal començar traient x2 en factor ja que el polinomi no té terme independent; la 1a arrel doble és zero.

Després aplica el mètode de Ruffini al polinomi de grau 3 que has trobat.

 

]]> Si apliques el mètode de Ruffini al polinomi que has trobat traient x2 en factor, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»P«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/mrow»«/mstyle»«/math», trobes la 3a arrel, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«/mrow»«/mstyle»«/math».

El quocient del mètode de Ruffini és un polinomi de 2n grau amb dues solucions, la 4a i la 5a arrel.

]]> 1.2.4.80DT MCM I MCD  

mcm i mcd de diferents polinomis

El mcm de diferents polinomis es calcula multiplicant entre ells tots els factors comuns i no comuns elevats a l'exponent màxim de les factoritzacions.

El mcd de diferents polinomis es calcula multiplicant entre ells exclusivament els factors comuns elevats a l'exponent mínim de les factoritzacions.



]]> 0.0000000 0.0000000 0 1.2.4.81Q M.C.D. G3G4 SenseTI Calcula el màxim comú divisor dels polinomis
P(x) = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»nm«/mi»«/mrow»«/mstyle»«/math» i Q(x) = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»dn«/mi»«/mrow»«/mstyle»«/math».
Escriu el resultat com un producte de factors.
]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nm</mi><mo>:</mo><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>a2</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b1</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mo>(</mo><mo> </mo><mi>a1</mi><mo>=</mo><mi>b1</mi><mo> </mo><mo>∨</mo><mo> </mo><mi>a1</mi><mo>=</mo><mi>b2</mi><mo> </mo><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dn</mi><mo>:</mo><mo>=</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b1</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>mcd</mi><mo>(</mo><mi>nm</mi><mo>,</mo><mi>dn</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>m</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>nm</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q1</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>dn</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nm</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>24</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dn</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>15</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> La factorització dels polinomis ens dona:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»P«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»Q«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/mrow»«/mstyle»«/math»

només cal escollir els factors comuns amb l'exponent més petit.

]]> 1.2.4.82Q M.C.D. G3G3 Calcula el màxim comú divisor dels polinomis
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»nm«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»dn«/mi»«/mrow»«/mstyle»«/math».
Escriu el resultat com un producte de factors.
]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nm</mi><mo>:</mo><mo>=</mo><mi>a</mi><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a2</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b2</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b3</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr></mtable><mrow><mo>(</mo><mo> </mo><mi>a1</mi><mo>=</mo><mi>b1</mi><mo> </mo><mo>∨</mo><mo> </mo><mi>a1</mi><mo>=</mo><mi>b2</mi><mo> </mo><mo>∨</mo><mo> </mo><mi>a1</mi><mo>=</mo><mi>b3</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dn</mi><mo>:</mo><mo>=</mo><mi>b</mi><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b1</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b2</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>mcd</mi><mo>(</mo><mi>nm</mi><mo>,</mo><mi>dn</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>m</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>nm</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q1</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>dn</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nm</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>35</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>30</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dn</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>24</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>24</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> La factorització dels polinomis és:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»P«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»Q«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/mrow»«/mstyle»«/math»

només cal agafar els factors comuns amb l'exponent més petit

]]> 1.2.4.85Q M.C.M. G3G4 SenseTI Calcula el mínim comú múltiple dels polinomis
P(x) = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»nm«/mi»«/mrow»«/mstyle»«/math» i Q(x) = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»dn«/mi»«/mrow»«/mstyle»«/math».
Escriu el resultat com un producte de factors.
]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nm</mi><mo>:</mo><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>a2</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b1</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mo>(</mo><mo> </mo><mi>a1</mi><mo>=</mo><mi>b1</mi><mo> </mo><mo>∨</mo><mo> </mo><mi>a1</mi><mo>=</mo><mi>b2</mi><mo> </mo><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dn</mi><mo>:</mo><mo>=</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b1</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>mcm</mi><mo>(</mo><mi>nm</mi><mo>,</mo><mi>dn</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>m</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>nm</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q1</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>dn</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nm</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>9</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dn</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>18</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><mfenced><mrow><mo>-</mo><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfenced><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>5</mn></msup><mo>-</mo><mn>12</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>18</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> La factorització dels polinomis  dona:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»P«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»Q«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/mrow»«/mstyle»«/math»

Agafa TOTS els factors amb l'exponent més GRAN

]]> 1.2.4.86Q M.C.M. G3G3 Calcula el mínim comú múltiple dels polinomis
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»nm«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»dn«/mi»«/mrow»«/mstyle»«/math».
Escriu el resultat com un producte de factors.
]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nm</mi><mo>:</mo><mo>=</mo><mi>a</mi><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a2</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b2</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b3</mi><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr></mtable><mrow><mo>(</mo><mo> </mo><mi>a1</mi><mo>=</mo><mi>b1</mi><mo> </mo><mo>∨</mo><mo> </mo><mi>a1</mi><mo>=</mo><mi>b2</mi><mo> </mo><mo>∨</mo><mo> </mo><mi>a1</mi><mo>=</mo><mi>b3</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dn</mi><mo>:</mo><mo>=</mo><mi>b</mi><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b1</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b2</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>mcm</mi><mo>(</mo><mi>nm</mi><mo>,</mo><mi>dn</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>m</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>nm</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q1</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>dn</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nm</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>35</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>30</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dn</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>24</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>24</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> La factorització dels polinomis és:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»P«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»Q«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/mrow»«/mstyle»«/math»

Agafa TOTS factors  amb l'exponent més GRAN

]]> 1rBTX 02. POLINOMIS/1.2.5 Fraccions algèbriques 1.2.5.10DT SIMPLIFICA FA  

Simplifica fraccions algèbriques

Per simplificar fraccions algèbriques, dividim el seu numerador i el seu denominador per el mcd d'ambdós.

A la practica, "tatxem" els factors repetits al numerador i al denominador si TOTS els factors s'estant multiplicant entre ells; MAI si s'estan sumant.

 



]]> 0.0000000 0.0000000 0 1.2.5.11Q SimplificaFA G3G3  Simplifica la fracció «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»P«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»Q«/mi»«/mrow»«/mfrac»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a3</mi><mo>≠</mo><mi>b3</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>:</mo><mo>=</mo><mi>a</mi><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a2</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>:</mo><mo>=</mo><mi>b</mi><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b2</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mi>P</mi><mi>Q</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>P</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q1</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>Q</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>21</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>18</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow><mrow><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>6</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfenced><mn>2</mn></msup><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Cal factoritzar el numerador i el denominador per simplificar:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»P«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»Q«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»P«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»Q«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/math»

]]> 1.2.5.12Q SimplificaFA G4G4 amb arrel num i den Simplifica la fracció:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»M«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»N«/mi»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

sabent que  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«/mstyle»«/math»  són arrels del numerador i del denominador.

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>36</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>256</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>768</mn></mtd></mtr></mtable></mfenced><mrow><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>114</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>522</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>648</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>16</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>64</mn></mrow><mrow><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>54</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Factoritza el numerador i el denominador:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»M«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»N«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

Ja pots simplificar

]]> 1.2.5.20DT SUMA FA Suma de fraccions algèbriques

Primer cal reduir-les al mínim comú denominador que és el polinomi mcm dels denominadors (Tots els factors amb l'exponent més gran)

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#191919¨»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»5«/mn»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#191919¨»+«/mo»«mfrac mathcolor=¨#191919¨»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»25«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#191919¨»=«/mo»«mfrac mathcolor=¨#191919¨»«mrow»«mfenced»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathcolor=¨#0000FF¨ mathvariant=¨bold¨»(«/mo»«mi mathcolor=¨#0000FF¨ mathvariant=¨bold¨»x«/mi»«mo mathcolor=¨#0000FF¨ mathvariant=¨bold¨»+«/mo»«mn mathcolor=¨#0000FF¨ mathvariant=¨bold¨»5«/mn»«mo mathcolor=¨#0000FF¨ mathvariant=¨bold¨»)«/mo»«/mrow»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»5«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathcolor=¨#0000FF¨ mathvariant=¨bold¨»(«/mo»«mi mathcolor=¨#0000FF¨ mathvariant=¨bold¨»x«/mi»«mo mathcolor=¨#0000FF¨ mathvariant=¨bold¨»+«/mo»«mn mathcolor=¨#0000FF¨ mathvariant=¨bold¨»5«/mn»«mo mathcolor=¨#0000FF¨ mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#191919¨»+«/mo»«mfrac mathcolor=¨#191919¨»«mrow»«mfenced»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfenced»«mi mathcolor=¨#FF0000¨ mathvariant=¨bold¨»x«/mi»«/mrow»«mrow»«mi mathcolor=¨#FF0000¨ mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»5«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»5«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

Quan tenen el mateix denominador, es sumen els numeradors.

]]> 0.0000000 0.0000000 0 1.2.5.21Q SumaFA G1G1 Primers Suma les fraccions: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #r_11]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>a_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_4</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>a_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mi>F</mi><mo>+</mo><mi>G</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>n1</mi><mo>*</mo><mi>d2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi><mo>=</mo><mi>n2</mi><mo>*</mo><mi>d1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d5</mi><mo>=</mo><mo>(</mo><mi>mcm</mi><mo>(</mo><mi>b_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>,</mo><mi>a_5</mi><mo>,</mo><mi>a_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>5</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>16</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>11</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que els denominadors #d1 i #d2 no tenen cap divisor comú, el mcm per realitzar la suma és (#d1)·(#d2).

L'expressió es transforma en: 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mfenced mathcolor=¨#FF0000¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced mathcolor=¨#FF0000¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mfenced mathcolor=¨#FF0000¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced mathcolor=¨#FF0000¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«/math»

Ara ja tenen el mateix denominador i es poden sumar els numeradors:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«/math»

]]> 1.2.5.22Q SumaFA G1G1 NoPrimers Suma les fraccions: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi><mo>=</mo><mi>n2</mi><mo>*</mo><mi>d1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d5</mi><mo>=</mo><mo>(</mo><mi>mcm</mi><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_3</mi><mo>)</mo><mo>)</mo><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mi>b_2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mo>(</mo><mi>mcm</mi><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_3</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k11</mi><mo>=</mo><mfrac><mi>k1</mi><mi>b_1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k12</mi><mo>=</mo><mfrac><mi>k1</mi><mi>b_3</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d11</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>b_2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>7</mn></mrow><mrow><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>8</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></mrow><mrow><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>12</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>24</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>22</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>15</mn></mrow><mrow><mn>12</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>24</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">8</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que els denominadors «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»d«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»d«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«/mrow»«/mstyle»«/math» són múltiples de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfenced»«/mstyle»«/math»,

el denominador comú per  la suma és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»k«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»d«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»11«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«/mrow»«/mstyle»«/math»

L'expressió es transforma en: 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«mn mathvariant=¨bold¨»12«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

Ara ja tenen el mateix denominador i es pot calcular el numerador, multiplicant i sumant.

 

]]> 1.2.5.23Q SumaFA G1G2 NoPrimers Suma les fraccions: F(x) + G(x) 

amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«/mrow»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>9</mn></mtd></mtr></mtable></mfenced><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>9</mn></mtd></mtr></mtable></mfenced><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_1</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_6</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mfrac><mi>b_2</mi><mi>b_1</mi></mfrac><mo>≠</mo><mfrac><mi>b_4</mi><mi>b_3</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfrac><mi>b_2</mi><mi>b_1</mi></mfrac><mo>≠</mo><mfrac><mi>a_2</mi><mi>a_1</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfrac><mi>b_4</mi><mi>b_3</mi></mfrac><mo>≠</mo><mfrac><mi>a_4</mi><mi>a_3</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>b_2</mi><mo>≠</mo><mfrac><mi>a_4</mi><mi>a_3</mi></mfrac></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>a_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_2</mi><mo>)</mo></mrow><mrow><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>a_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d11</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>d1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>a_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_4</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo><mo>*</mo><mi>b_6</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mo>(</mo><mi>a_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mo>(</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo><mo>*</mo><mi>b_6</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d21</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>d2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc1</mi><mo>=</mo><mi>mcm</mi><mo>(</mo><mi>d1</mi><mo>,</mo><mi>d2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc11</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>mc1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>quocient</mi><mo>(</mo><mi>mc1</mi><mo>,</mo><mi>d1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>p11</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>quocient</mi><mo>(</mo><mi>mc1</mi><mo>,</mo><mi>d2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>p21</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>F</mi><mo>+</mo><mi>G</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi><mo>=</mo><mi>n1</mi><mo>*</mo><mi>p11</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi><mo>=</mo><mi>n2</mi><mo>*</mo><mi>p21</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>,</mo><mi>a_5</mi><mo>,</mo><mi>a_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>18</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>9</mn></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>13</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que #d1 = #d11

i que #d2 = #d21,

 

el mcm dels denominadors és #mc11.

 

]]> Si el mcm dels denominadors és  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»mc«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»11«/mn»«/mrow»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=a409f4635fdb01c84b8b95b96ed1568f&cw=46&ch=10&cb=9" style="vertical-align: -1px;"/>, la suma s'escriu:


«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»21«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»mc«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»mc«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfrac»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=e99ead11a57c6034b2d2d5fd8c01bfbd&cw=303&ch=27&cb=18" style="vertical-align: -9px;"/>

]]> 1.2.5.24Q SumaFa G1G2 Primers Suma les fraccions: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mfrac><mi>b_2</mi><mi>b_1</mi></mfrac><mo>≠</mo><mfrac><mi>b_4</mi><mi>b_3</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>b_1</mi><mo> </mo><mi>mod</mi><mo> </mo><mi>b_3</mi><mo> </mo><mo>≠</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfrac><mi>b_2</mi><mi>b_1</mi></mfrac><mo>≠</mo><mfrac><mi>a_2</mi><mi>a_1</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfrac><mi>b_4</mi><mi>b_3</mi></mfrac><mo>≠</mo><mfrac><mi>a_4</mi><mi>a_3</mi></mfrac></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>a_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_2</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>b_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>a_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_4</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><msup><mo>)</mo><mn>2</mn></msup></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>F</mi><mo>+</mo><mi>G</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>,</mo><mi>a_5</mi><mo>,</mo><mi>a_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mi>a_5</mi><mo>,</mo><mi>a_6</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></mrow><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow><mrow><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>18</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>9</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>27</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>34</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>19</mn></mrow><mrow><mn>18</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>27</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>9</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que no tenen cap factor en comú, el denominador comú (mcm) és el producte dels dos denominadors.

]]> 1.2.5.25Q SumaFA G2G2 NoPrimers Suma les fraccions: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mfrac><mi>b_2</mi><mi>b_1</mi></mfrac><mo>≠</mo><mfrac><mi>b_4</mi><mi>b_3</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>b_1</mi><mo> </mo><mi>mod</mi><mo> </mo><mi>b_3</mi><mo> </mo><mo>≠</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfrac><mi>b_2</mi><mi>b_1</mi></mfrac><mo>≠</mo><mfrac><mi>a_2</mi><mi>a_1</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfrac><mi>b_4</mi><mi>b_3</mi></mfrac><mo>≠</mo><mfrac><mi>a_4</mi><mi>a_3</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>b_2</mi><mo>≠</mo><mfrac><mi>a_4</mi><mi>a_3</mi></mfrac></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>a_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_2</mi><mo>)</mo></mrow><mrow><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>a_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_4</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo><mo>*</mo><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>F</mi><mo>+</mo><mi>G</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>mcm</mi><mfenced><mrow><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo><mo>,</mo><mo>(</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo><mo>*</mo><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d11</mi><mo>=</mo><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d12</mi><mo>=</mo><mo>(</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo><mo>*</mo><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fn</mi><mo>=</mo><mi>factoritza</mi><mfenced><mrow><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fd</mi><mo>=</mo><mi>factoritza</mi><mfenced><mrow><mo>(</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo><mo>*</mo><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>,</mo><mi>a_5</mi><mo>,</mo><mi>a_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>,</mo><mi>a_5</mi><mo>,</mo><mi>a_6</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></mrow><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></mrow><mrow><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>24</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>21</mn></mrow><mrow><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>24</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>24</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fn</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fd</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Les factoritzacions dels denominadors són:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»d«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»11«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»fn«/mi»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»d«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»12«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»fd«/mi»«mspace linebreak=¨newline¨/»«/mrow»«/mstyle»«/math»

el seu mcm, i per tant el denominador comú és:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»w«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/mrow»«/mstyle»«/math»

]]> 1.2.5.26Q SumaFA G2G2 NoPrimers IdRemarcable Suma les fraccions: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>F</mi><mo>+</mo><mi>G</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d11</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>d1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d21</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>d2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc1</mi><mo>=</mo><mi>mcm</mi><mo>(</mo><mi>d1</mi><mo>,</mo><mi>d2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc11</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>mc1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>quocient</mi><mo>(</mo><mi>mc1</mi><mo>,</mo><mi>d1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>quocient</mi><mo>(</mo><mi>mc1</mi><mo>,</mo><mi>d2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi><mo>=</mo><mi>n1</mi><mo>*</mo><mi>p1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi><mo>=</mo><mi>n2</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>n1</mi><mo>,</mo><mi>d1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>125</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>n2</mi><mo>,</mo><mi>d2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn><mo>,</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>20</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>50</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></mrow><mrow><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>125</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></mrow><mrow><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>20</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>50</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>21</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>66</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>45</mn></mrow><mrow><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>50</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>250</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1250</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>5</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>50</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>250</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1250</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>5</mn></mrow></mfenced><mo>*</mo><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>24</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>30</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>90</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>75</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»d«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»d«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»11«/mn»«/mrow»«/mstyle»«/math»

i «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»d«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»d«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»21«/mn»«/mrow»«/mstyle»«/math», 

el denominador comú és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»mc«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»11«/mn»«/mrow»«/mstyle»«/math».

]]> Si el denominador comú és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»mc«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»11«/mn»«/mrow»«/mstyle»«/math»,

la suma es transforma en:

 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»21«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced mathcolor=¨#FF0000¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»)«/mo»«/mrow»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»)«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«msup»«mo mathvariant=¨bold¨»)«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mfenced mathcolor=¨#FF0000¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfenced»«mfenced mathcolor=¨#FF0000¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»)«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«msup»«mo mathvariant=¨bold¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»)«/mo»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

]]> 1.2.5.31Q RestaFA G1G1 Primers Resta les fraccions F(x) – G(x)

amb  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_1</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mfrac><mi>b_2</mi><mi>b_1</mi></mfrac><mo>≠</mo><mfrac><mi>b_4</mi><mi>b_3</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfrac><mi>b_2</mi><mi>b_1</mi></mfrac><mo>≠</mo><mfrac><mi>a_2</mi><mi>a_1</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfrac><mi>b_4</mi><mi>b_3</mi></mfrac><mo>≠</mo><mfrac><mi>a_4</mi><mi>a_3</mi></mfrac></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>a_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_2</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>b_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>a_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>b_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>a_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_4</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>a_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>F</mi><mo>-</mo><mi>G</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>n1</mi><mo>*</mo><mi>d2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi><mo>=</mo><mi>n2</mi><mo>*</mo><mi>d1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d5</mi><mo>=</mo><mo>(</mo><mi>mcm</mi><mo>(</mo><mi>b_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>,</mo><mi>a_5</mi><mo>,</mo><mi>a_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>5</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>16</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que els denominadors #d1 i #d2 no tenen cap divisor comú, el mcm per realitzar la suma és (#d1)·(#d2).

L'expressió es transforma en: 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mfenced mathcolor=¨#FF0000¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced mathcolor=¨#FF0000¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mfenced mathcolor=¨#FF0000¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced mathcolor=¨#FF0000¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

Ara ja tenen el mateix denominador i es poden sumar els numeradors:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«/mrow»«/mstyle»«/math»

]]> 1.2.5.32Q RestaFA G1G2 NoPrimers Resta les fraccions: F(x) – G(x) 

amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«/mrow»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable 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xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfrac></math></output></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>18</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>9</mn></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>13</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que #d1 = #d11

i que #d2 = #d21,

 

el mcm dels denominadors és #mc11.

 

]]> Si el mcm dels denominadors és  #mc11, la resta s'escriu:


«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»21«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»mc«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»mc«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

]]> 1.2.5.33Q RestaFA G2G2 NoPrimers Resta les fraccions F(x) – G(x)

amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mfrac><mi>b_2</mi><mi>b_1</mi></mfrac><mo>≠</mo><mfrac><mi>b_4</mi><mi>b_3</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>b_1</mi><mo> </mo><mi>mod</mi><mo> </mo><mi>b_3</mi><mo> </mo><mo>≠</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfrac><mi>b_2</mi><mi>b_1</mi></mfrac><mo>≠</mo><mfrac><mi>a_2</mi><mi>a_1</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfrac><mi>b_4</mi><mi>b_3</mi></mfrac><mo>≠</mo><mfrac><mi>a_4</mi><mi>a_3</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>b_2</mi><mo>≠</mo><mfrac><mi>a_4</mi><mi>a_3</mi></mfrac></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>a_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_2</mi><mo>)</mo></mrow><mrow><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>a_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_4</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo><mo>*</mo><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>F</mi><mo>-</mo><mi>G</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>mcm</mi><mfenced><mrow><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo><mo>,</mo><mo>(</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo><mo>*</mo><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d11</mi><mo>=</mo><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d12</mi><mo>=</mo><mo>(</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo><mo>*</mo><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fn</mi><mo>=</mo><mi>factoritza</mi><mfenced><mrow><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fd</mi><mo>=</mo><mi>factoritza</mi><mfenced><mrow><mo>(</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo><mo>*</mo><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>,</mo><mi>a_5</mi><mo>,</mo><mi>a_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mi>a_5</mi><mo>,</mo><mi>a_6</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></mrow><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow><mrow><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>20</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>16</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>9</mn></mrow><mrow><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>20</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>16</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>20</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>16</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fn</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fd</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Les factoritzacions dels denominadors són:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»d«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»11«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»fn«/mi»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»d«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»12«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»fd«/mi»«mspace linebreak=¨newline¨/»«/mrow»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=1edb4609d30bbc06c8d62d7a287ecfb9&cw=84&ch=27&cb=22" style="vertical-align: -5px;"/>

el seu mcm, i per tant el denominador comú és:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»w«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/mrow»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=28a71b18b9f3136cf9717240d2845cd5&cw=31&ch=10&cb=9" style="vertical-align: -1px;"/>

]]> 1.2.5.40DT PRODUCTE FA Multiplicació de fraccions algèbriques

Es presenta el numerador de la 1a multiplicat pel numerador de la 2a i el denominador de la 1a multiplicat pel denominador de la 2a:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfrac mathcolor=¨#003300¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«/mfenced»«/mrow»«/mfrac»«/mstyle»«/math»

Es factoritza el numerador i el denominador per simplificar:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfrac mathcolor=¨#003300¨»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«/mstyle»«/math»

]]> 0.0000000 0.0000000 0 1.2.5.41Q MultiplicaFA G1G1 Simplificable Multiplica les fraccions:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«/mrow»«/mstyle»«/math»

Resultat simplificat i factoritzat

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n1</mi><mo>=</mo><mi>a_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a_2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>a_1</mi><mo>*</mo><mo>(</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>n1</mi><mo>,</mo><mi>d1</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>n2</mi><mo>,</mo><mi>d2</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mfrac><mrow><mi>a_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a_2</mi><mo>)</mo></mrow><mrow><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow><mrow><mi>a_1</mi><mo>*</mo><mo>(</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>n1</mi><mo>*</mo><mi>n2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><mi>d1</mi><mo>*</mo><mi>d2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc1</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>mcd</mi><mo>(</mo><mi>n3</mi><mo>,</mo><mi>d3</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>n3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>d3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f5</mi><mo>=</mo><mi>factoritza</mi><mfenced><mrow><mi>b_1</mi><mo>*</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_1</mi><mo>*</mo><mi>b_4</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mi>a_2</mi></mrow><mi>f5</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>,</mo><mi>a_5</mi><mo>,</mo><mi>a_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>7</mn><mo>,</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>9</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>36</mn></mrow><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow><mrow><mn>36</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>36</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow><mrow><mn>8</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>9</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>108</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>144</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>216</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> a) Es fa la multiplicació:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

b) Es factoritza el numerador: #f1

es factoritza el denominador:  #f2

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

i es simplifica pel seu mcd que és #mc1

]]> 1.2.5.42Q MultiplicaFA G2G2 Simplificable Multiplica les fraccions: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»amb«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«/mrow»«/mstyle»«/math»

Resultat simplificat

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b4</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b6</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>n1</mi><mo>,</mo><mi>d1</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>n2</mi><mo>,</mo><mi>d2</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a2</mi><mo>≠</mo><mi>b4</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a2</mi><mo>≠</mo><mi>b6</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mfrac><mrow><mi>a1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a2</mi><mo>)</mo></mrow><mrow><mi>b1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b2</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mi>b2</mi><mo>)</mo></mrow><mrow><mi>a1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b4</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b6</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>n1</mi><mo>*</mo><mi>n2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><mi>d1</mi><mo>*</mo><mi>d2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc1</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>mcd</mi><mo>(</mo><mi>n3</mi><mo>,</mo><mi>d3</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>F</mi><mo>*</mo><mi>G</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>n3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>d3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df3</mi><mo>=</mo><mi>b1</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b1</mi><mo>*</mo><mo>(</mo><mi>b4</mi><mo>+</mo><mi>b6</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>b1</mi><mo>*</mo><mi>b4</mi><mo>*</mo><mi>b6</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi><mo>=</mo><mi>factoritza</mi><mfenced><mi>df3</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mi>a2</mi></mrow><mi>f3</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>7</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>28</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow><mrow><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>21</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>70</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>,</mo><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow><mrow><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></mrow></mfrac><mo>,</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>10</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>112</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>154</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>280</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df3</mi><mo>,</mo><mi>f3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>10</mn><mo>,</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">8</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> a) Es fa la multiplicació:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«/math»

b) Es factoritza el numerador: #f1

es factoritza el denominador:  #f2

i es simplifica pel seu mcd que és #mc1

]]> 1.2.5.50DT DIVISIÓ FA Divisió de fraccions algèbriques

Es multiplica la 1a per la inversa de la segona:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«mrow»«mi»x«/mi»«mo»+«/mo»«mn»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«/mfenced»«/mrow»«/mfrac»«/mstyle»«/math»

Es factoritza el numerador i el denominador per simplificar:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«/mstyle»«/math»

]]> 0.0000000 0.0000000 0 1.2.5.51Q DivisióFA G1G1 Simplificable Divideix «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»:«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»amb«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«/mrow»«/mstyle»«/math»

Resultat simplificat i factoritzat

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>5</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">8</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer es multiplica la primera fracció per la inversa de la segona:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#0000FF¨»«mrow»«mi mathvariant=¨bold¨»F«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«mrow»«mi mathvariant=¨bold¨»G«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

Després es factoritza

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#0000FF¨»«mrow»«mi mathvariant=¨bold¨»F«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«mrow»«mi mathvariant=¨bold¨»G«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfrac»«/mstyle»«/math»

i es simplifica

]]> 1.2.5.52Q DivisióFA G2G2 Simplificable Divideix «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»:«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»amb«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mfrac><mi>n1</mi><mi>d1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mfrac><mi>n2</mi><mi>d2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>n1</mi><mo>*</mo><mi>d2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>d1</mi><mo>*</mo><mi>n2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n51</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>b4</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a3</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b6</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n52</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>a4</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b3</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a6</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mi>n51</mi><mi>n52</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mfrac><mi>F</mi><mi>G</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>77</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>126</mn></mrow><mrow><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>50</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>105</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>28</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>84</mn></mrow><mrow><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>48</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>108</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>4</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>9</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>9</mn></mrow></mfenced></mrow><mrow><mn>5</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>7</mn></mrow></mfenced></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>324</mn></mrow><mrow><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>65</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>210</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>28</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>9</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>9</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>35</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>7</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n51</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>9</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>9</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">6</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer es multiplica la primera fracció per la inversa de la segona:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#0000FF¨»«mrow»«mi mathvariant=¨bold¨»F«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«mrow»«mi mathvariant=¨bold¨»G«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

Després es factoritza i es simplifica:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfrac»«/mstyle»«/math»

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