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682b4b47-b077-4956-911b-d772e9c8a38c.html
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<p><strong><em>Students will complete the following questions to practice the skills they have learned in this lesson.</em></strong></p>
<ol class="os-raise-noindent">
<li>Choose the expression that best describes the diagram.<br> </li>
</ol>
<br>
<img alt class="img-fluid atto_image_button_text-bottom" height="124" role="presentation" src="https://k12.openstax.org/contents/raise/resources/a4c39cadbd12167dc25e8a8977547823585c8403" width="254">
<ul>
<li>\((2x+5)(x+3)\) is equivalent to \(2x^2+5x+8\). </li>
<li>\((2x +5)(x +3)\) is equivalent to \(2x^2+14x + 23\). </li>
<li>\((2x+5)(x+3)\) is equivalent to \(2x^2+11x+15\). </li>
<li>\((2x +5)(x +3)\) is equivalent to \(30x^2\). </li>
</ul>
<p><strong>Answer: </strong>\((2x+5)(x+3)\) is equivalent to \(2x^2+11x+15\). </p>
<ol class="os-raise-noindent" start="2">
<li>In questions a–d, match each expanded quadratic expression with an equivalent expression written as a product.</li>
</ol>
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" type="a">
<li>\(x^2+12x+32\)
<ul>
<li>\((x+2)(x+6)\) </li>
<li> \((x+4)(x+2)\)</li>
<li> \((x+8)(x+4)\)</li>
<li>\((x+2)(x+3)\)</li>
</ul>
</li>
</ol>
</ol>
<strong> </strong>
<p><strong>Answer: </strong>\((x+8)(x+4)\)</p>
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="2" type="a">
<li> \(x^2+5x+6\)
<ul>
<li> \((x+2)(x+6)\) </li>
<li> \((x+4)(x+2)\) </li>
<li> \((x+8)(x+4)\) </li>
<li> \((x+2)(x+3)\) </li>
</ul>
</li>
</ol>
</ol>
<p><strong>Answer:</strong> \((x+2)(x+3)\)</p>
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="3" type="a">
<li>\(x^2+6x+8\)
<ul>
<li> \((x+2)(x+6)\) </li>
<li> \((x+4)(x+2)\) </li>
<li> \((x+8)(x+4)\) </li>
<li> \((x+2)(x+3)\) </li>
</ul>
</li>
</ol>
</ol>
<p><strong>Answer:</strong> \((x+4)(x+2)\)</p>
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="4" type="a">
<li>\(x^2+8x+12\)
<ul>
<li>\( (x+2)(x+6)\)</li>
<li> \((x+4)(x+2)\)</li>
<li> \((x+8)(x+4)\)</li>
<li> \((x+2)(x+3)\)</li>
</ul>
</li>
</ol>
</ol>
<p><strong>Answer:</strong> \((x+2)(x+6)\)</p>
<ol class="os-raise-noindent" start="3">
<li><strong>Select three</strong> expressions that are equivalent to \(x^2+4x\). </li>
</ol>
<ul>
<li> \(x(x+4)\) </li>
<li> \((x+2)^2\) </li>
<li> \((x+x)(x+4)\) </li>
<li>\((x+2)^2-4\) </li>
<li>\((x+4)x\) </li>
</ul>
<p><strong>Answer:</strong> \(x(x+4)\), \((x+2)^2-4\), \((x+4)x\)</p>
<ol class="os-raise-noindent" start="4">
<li>Tyler drew a diagram to expand \((x+5)(2x+3)\).</li>
</ol>
<p><img alt="Rectangle partitioned into 4 smaller rectangles. The top is labeled 2 x and 3. The side is labeled x and 5. Inside, the top row contains 2 x squared and 3 x. The bottom row contains 7 x and 8." height="168" src="https://k12.openstax.org/contents/raise/resources/3257ad167a891e11df938a70502ad9c0fd909998" width="254"></p>
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" type="a">
<li> Tyler’s diagram is incorrect. Choose the sentence that describes Tyler’s mistake.
<ul>
<li> Tyler added 5 and 2 and 5 and 3 instead of multiplying them. </li>
<li> Tyler multiplied 5 and 2 and 5 and 3 instead of adding them. </li>
<li> Tyler should have labeled the top \(2x\) and 5 and the side \(x\) and 3. </li>
<li> Tyler should have labeled the top \(x\) and 3 and the side \(2x\) and 5. </li>
</ul>
</li>
</ol>
</ol>
<p><strong>Answer:</strong> Tyler added 5 and 2 and 5 and 3 instead of multiplying them. </p>
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="2" type="a">
<li> What is the correct expanded form of \((x+5)(2x+3)\)?
<ul>
<li>\(3x+8\)</li>
<li>\( 30x^2\) </li>
<li> \(2x^2+10x+8\) </li>
<li> \(2x^2+13x+15\) </li>
</ul>
</li>
</ol>
</ol>
<p><strong>Answer:</strong> \(2x^2+13x+15\)</p>