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0f5cca5d-b7a5-40f5-b351-0c91d76e51c7.html
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<h4>Activity </h4>
<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">
<p>Let’s factor this trinomial.</p>
<p>\(t^2 + 14t + 24\)</p>
<p>Think: <br>
What are the factors of \(24\)?<br>
Which of these factors add to \(14\)?</p>
<p>Here is the table we made in the previous activity:</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>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answers. Then select the <strong>solution</strong> button to compare your work.</p>
<p>You can use the following video if you need some help</p>
<div class="os-raise-d-flex-nowrap os-raise-justify-content-center">
<div class="os-raise-video-container"><video controls="true" crossorigin="anonymous">
<source src="https://k12.openstax.org/contents/raise/resources/4282f9c6585902ab44d89e3fa21ec7e9d5d984cd">
<track default="true" kind="captions" label="On" src="https://k12.openstax.org/contents/raise/resources/3f0ef0fc07a68dad49fa2a586a9a02043d8210e6" srclang="en_us">
</video></div>
</div><br>
</div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal1">
<p>Compare your answers:</p>
<p>\(2 \cdot 12 = 24\)<br>
\(2 + 12 = 14\)</p>
<p>So, use \(2\) and \(12\) as the last terms of the binomials.</p>
<p>\((t + 2)(t + 12)\)</p>
</div>
<p>Factor each trinomial. If the trinomial cannot be factored, write “prime.”</p>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="1b76b94c-180a-4f9c-8c96-658408e38bcc" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent">
<li>\(9m + m^2 + 18\) </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>\((m + 3)(m + 6)\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="b0eeec46-f03c-483e-b68c-1ad26f24b308" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2">
<li>\(a^2 − 11ab + 10b^2\) </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>\((a - b)(a - 10b)\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="8e965bcc-5e25-483c-bb7a-16ee2555d8ac" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3">
<li>\(u^2 - 9uv - 12v^2\) </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>prime</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="3e9ad423-73bf-4b27-b571-937b86f75c2b" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="4">
<li>\(5p − 6 + p^2\) </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>\((p − 1)(p + 6)\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="8e7d5d3f-5111-4f11-b7e6-a248afc16033" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="5">
<li>\(m^2 − 64mn − 65n^2\) </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>\((m + n)(m − 65n)\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<h4>Video: Factoring Trinomials of the Form \(x^2 + bx + c\)</h4>
<p>Watch the following video to learn more about how factor trinomials of the form \(x^2 + bx + c\).</p>
<div class="os-raise-d-flex-nowrap os-raise-justify-content-center">
<div class="os-raise-video-container"><video controls="true" crossorigin="anonymous">
<source src="https://k12.openstax.org/contents/raise/resources/b768d8c99b6a4d262b7d77626f7598859a277e53">
<track default="true" kind="captions" label="On" src="https://k12.openstax.org/contents/raise/resources/892dadf86a37130b7b56e4477a71799bee89bd87" srclang="en_us">https://k12.openstax.org/contents/raise/resources/b768d8c99b6a4d262b7d77626f7598859a277e53
</video></div>
</div>