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<h4>Warm Up Activity</h4>
<p>In this unit, remember to double click on mathematical expressions/equations to enlarge, if needed.</p>
<p>We are going to factor the trinomial \(q^2 + 10q + 24\) by reversing the process of FOIL.</p>
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal1" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<ol class="os-raise-noindent">
<li>Find all the different combinations of factors of \(24\). One example is provided in the table.</li>
</ol>
<table class="os-raise-midsizetable">
<thead>
<tr>
<th scope="col"> Factors of 24</th>
<th scope="col"> Sum of factors</th>
</tr>
</thead>
<tbody>
<tr>
<td><p>\(1, 24\)</p></td>
<td><p>\(1 + 24 = 25\)</p></td>
</tr>
<tr>
<td> </td>
<td> </td>
</tr>
<tr>
<td> </td>
<td> </td>
</tr>
<tr>
<td> </td>
<td> </td>
</tr>
</tbody>
</table>
<br>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answers. Then select the <strong>solution</strong> button to compare your work. </p>
</div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal1">
<p>Compare your answers:</p>
<table class="os-raise-midsizetable">
<thead>
<tr>
<th scope="col"> Factors of 24</th>
<th scope="col"> Sum of factors</th>
</tr>
</thead>
<tbody>
<tr>
<td><p>\(1\), \(24\)</p></td>
<td><p>\(1 + 24 = 25\)</p></td>
</tr>
<tr>
<td><p>\(2\), \(12\)</p></td>
<td><p>\(2 + 12 = 14\)</p></td>
</tr>
<tr>
<td><p>\(3\), \(8\)</p></td>
<td><p>\(3 + 8 = 11\)</p></td>
</tr>
<tr>
<td><p>\(4\), \(6\)</p></td>
<td><p>\(4 + 6 = 10\)</p></td>
</tr>
</tbody>
</table>
<br>
</div>
<br>
<p>We’re going to look at these factors to see which of them would fit in the boxes and multiply to make the trinomial \(q^2 + 10q + 24\) that we started with in the beginning.</p>
<p>\((q+\square)(q+\square)\)</p>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="889914a8-6008-4d54-a25e-1b3cdd609087" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2">
<li>Which pair of factors fits the situation? What is the factored expression?</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>\(4\), \(6\); \((q + 4)(q + 6)\)</p>
<p>So, by undoing FOIL, we found that the trinomial \(q^2 + 10q + 24\) factors to the expression \((q + 4)(q + 6)\).</p>
</div>
</div>
<!--Interaction End -->