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8124bb00-3406-49ca-a1be-d63afb6892a4.html
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<p>Complete the following questions to practice the skills you have learned in this lesson. Double click on mathematical expressions/equations to enlarge.</p>
<br>
<p>For questions 1 - 2, find the quotients using division.</p>
<!--Do not edit this div tag. It must surround the interaction block-->
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="7bb698b5-c7d8-4a33-93b2-3efea1d76203" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="2" data-schema-version="1.0">
<!--q1-->
<div class="os-raise-ib-pset-problem" data-content-id="af56f7e8-d1e7-434e-b3eb-e09a0a5bd450" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(-\frac{3y^3}{4x^3}\)" data-solution-options='["\\(-\\frac{3x^3}{4y^3}\\)", "\\(-\\frac{4y^3}{3x^3}\\)", "\\(-\\frac{3y^3}{4x^3}\\)", "\\(-\\frac{3}{4}x^3y^3\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol start="1" type="1">
<li>\(\frac{45x^5y^9}{-60x^8y^6}\)</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 6.3.1.
</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(-\frac{3y^3}{4x^3}\).
</p>
</div>
</div>
<!--q2-->
<div class="os-raise-ib-pset-problem" data-content-id="3bf78ebd-82c8-4f1f-8b4c-05ee2395ef08" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(24\)" data-solution-options='["\\(24\\)", "\\(-24x\\)", "\\(24y\\)", "\\(-24\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol start="2" type="1">
<li>\((48y-24x) \div (2y-x)\)</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 6.3.1.
</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(24\).
</p>
</div>
</div>
<!--q3-->
<div class="os-raise-ib-pset-problem" data-content-id="8c897ca2-721c-4794-b080-53466399c4be" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(m^2-10m+100\)" data-solution-options='["\\(m^2+10m\\)", "\\( m^2-100\\)", "\\(m^2+10m-100\\) ", "\\(m^2-10m+100\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<p>For questions 3 and 4, divide using long division.</p>
<ol start="3">
<li>\((m^3+1000) \div (m+10)\)</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 6.3.2. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(m^2-10m+100\).
</p>
</div>
</div>
<!--q4-->
<div class="os-raise-ib-pset-problem" data-content-id="da27cc16-8c18-479e-ae6f-af78cd8f76c1" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(25y^2-20y+16- \frac{128}{5y+4}\)" data-solution-options='["\\(25y^2-20y+16- \\frac{128}{5y+4}\\)", "\\(25y^2-20y+16- \\frac{64}{5y+4}\\)", "\\(25y^2+20y+16\\)", "\\(25y^2-20y+16\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol start="4" type="1">
<li>\((125y^3-64) \div (5y+4)\)</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 6.3.2.
</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(25y^2-20y+16- \frac{128}{5y+4}\). </p>
</div>
</div>
<!--q5-->
<div class="os-raise-ib-pset-problem" data-content-id="bf202dfc-071e-44eb-ab0e-101d9a6c3441" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\( b^2-5b+6\); remainder \(0\)" data-solution-options='["\\(b^2+5b\\); remainder \\(6\\)", "\\( b^2-5b+6\\); remainder \\(0\\)", "\\(b^2-5b\\); remainder \\(6\\)", "\\(b^2+5b-6\\); remainder \\(0\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<p>For questions 5 - 6, divide using synthetic division.</p>
<ol start="5">
<li>\((b^3-3b^2-4b+12) \div (b+2)\)</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 6.3.3. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \( b^2-5b+6\); remainder \(0\).
</p>
</div>
</div>
<!--q6-->
<div class="os-raise-ib-pset-problem" data-content-id="348c050e-ab7c-4194-ba9c-dc70001ba540" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(3x^3-2x^2-4x-2\); remainder \(0\)" data-solution-options='["\\(3x^3+2x^2+4x+2\\); remainder \\(0\\)", "\\(3x^3-20x^2-62x-180\\); remainder \\(0\\)", "\\(3x^3-2x^2-4x-2\\); remainder \\(0\\)", "\\(3x^3-2x^2-4x\\); remainder \\(-2\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol start="6" type="1">
<li>\((3x^4-11x^3+2x^2+10x+6) \div (x-3)\)</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 6.3.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(3x^3-2x^2-4x-2\); remainder \(0\). </p>
</div>
</div>
<!--q7-->
<div class="os-raise-ib-pset-problem" data-content-id="22d7851a-2f27-4df6-8c77-1829103c897a" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(x-9\)" data-solution-options='["\\(x+9\\)", "\\(x-12\\)", "\\(x-3\\)", "\\(x-9\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<p>For questions 7 and 8, use the following polynomial functions.</p>
<ul>
<li>\(f(x)=x^2-13x+36\)<br>
</li>
<li>\(g(x)=x-4\)</li>
</ul>
<ol start="7">
<li>Find \((\frac{f}{g})(x)\).</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 6.3.4.
</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(x-9\).
</p>
</div>
</div>
<!--q8-->
<div class="os-raise-ib-pset-problem" data-content-id="bc2aeeea-7d9b-4b1b-9759-b1227a6756df" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\( -10\)" data-solution-options='["\\(-8\\)", "\\( -10\\)", "\\( -4\\)", "\\( 8\\) "]'>
<div class="os-raise-ib-pset-problem-content">
<ol start="8" type="1">
<li>Find \((\frac{f}{g})(-1)\).</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 6.3.4.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is –10. </p>
</div>
</div>
<!--Q9-->
<div class="os-raise-ib-pset-problem" data-content-id="932f9bd3-9a6c-4230-9522-bcfc683c8ce7" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="3" data-solution-options='["3", "21", "-13", "-9"]'>
<div class="os-raise-ib-pset-problem-content">
<ol start="9">
<li>Use the Remainder Theorem to find the remainder.
<p>\(f(x)=x^2-4x-9\) is divided by \(x + 2\)</p>
</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 6.3.5. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 3. </p>
</div>
</div>
<!--q10-->
<div class="os-raise-ib-pset-problem" data-content-id="ef170a4b-4c96-4a7e-9036-fcf0b2a55c3a" data-problem-type="multiplechoice" data-retry-limit="1" data-solution="Yes" data-solution-options='["Yes", "No"]'>
<div class="os-raise-ib-pset-problem-content">
<ol start="10">
<li>Use the Factor Theorem to determine if \(x-3\) is a factor of the \(x^3-7x^2+11x+3\).<br>
</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 6.3.5.
</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is yes. </p>
</div>
</div>
<!--Do not edit below this line-->
<div class="os-raise-ib-pset-correct-response"> </div>
<div class="os-raise-ib-pset-encourage-response"> </div>
</div>