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    <name>
      <text>1.3.4.2 Numerical factors</text>
    </name>
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      <text><![CDATA[<p class="HELM_exercise">Exercise</p>
<p>Factorise:<br></p>

<ol class="HELM_parts">

<li><p> \( {@a1@}x + {@a2@}y =\) [[input:ans1]] [[validation:ans1]] [[feedback:prt1]]</p></li>

<li><p> \( {@b1@}x - {@b2@}y =\) [[input:ans2]] [[validation:ans2]] [[feedback:prt2]]</p></li>

<li><p> \( {@c1@}x + {@c2@}y =\) [[input:ans3]] [[validation:ans3]] [[feedback:prt3]]</p></li>

<li><p> \( {@d1@}x + {@d2@}z + {@d3@}y =\) [[input:ans4]] [[validation:ans4]] [[feedback:prt4]]</p></li>

</ol>]]></text>
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      <text><![CDATA[<ol class="HELM_parts">
    <li>
        <p></p><p>We observe that there is a common factor of \({@a1@}\). Thus</p><p>\[&nbsp;{@a1@}x + {@a2@}y = {@ta1@}.\]</p><p></p>
    </li>
    <li>
        <p><span style="font-size: 0.9375rem;"></span></p><p>We observe that there is a common factor of \({@b1@}\). Thus</p><p>\[&nbsp;{@b1@}x - {@b2@}y = {@ta2@}.\]</p><p></p>
    </li>
    <li>
        <p><span style="font-size: 0.9375rem;"></span></p><p>We observe that there is a common factor of \({@c1@}\). Thus</p><p>\[&nbsp;{@c1@}x + {@c2@}y = {@ta3@}.\]<span style="font-size: 0.9375rem;">&nbsp;</span></p></li><li><p>We observe that there is a common factor of \({@d1@}\). Thus</p><p>\[ {@d1@}x + {@d2@}z + {@d3@}y= {@ta4@}.\]</p><p></p></li><br>&nbsp;</ol>]]></text>
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    <stackversion>
      <text>2021072200</text>
    </stackversion>
    <questionvariables>
      <text>a1: rand(2)+3;
am:rand(3)+3;
a2: am*a1;
ta1: a1*(x + am*y);

b1: rand(2)+3;
bm: b1;
b2:b1*bm
ta2: b1*(x - bm*y);

c1: rand([2,3]);
cm:rand([5,6]);
c2: cm*c1;
ta3: c1*(x + cm*y);

d1: rand([4,6]);
dm:rand([6,7]);
d2: dm*d1;
d3:(dm-3)*d1;
ta4: d1*(x + dm*z + (dm-3)*y);

e1:rand([3]);
e2:e1*2;
ta5:(1/e1)*(x + (1/2)*y);</text>
    </questionvariables>
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    <questionnote format="moodle_auto_format">
      <text>\({@ta1@}, {@ta2@}, {@ta3@}, {@ta4@}                \)</text>
    </questionnote>
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      <text/>
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      <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Correct answer, well done.]]></text>
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      <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
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      <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Incorrect answer.]]></text>
    </prtincorrect>
    <decimals>.</decimals>
    <scientificnotation>*10</scientificnotation>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
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					<div>
						<p></p></div></div></div></div><p>We observe that there is a common factor of \({@a1@}\). Thus</p><p>\[&nbsp;{@a1@}x + {@a2@}y = {@ta1@}.\]</p>]]></text>
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