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<title>Dividing Polynomials</title>
<meta name="description" content="Sometimes it is easy to divide a polynomial by splitting it at the + and − signs. We can also rearrange the top polynomial before dividing." />
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<h1 align="center">Dividing Polynomials</h1>
<p><span class="larger">A <a href="polynomials.html">polynomial</a> looks like this:</span> </p>
<div class="beach">
<table border="0" align="center" cellpadding="5">
<tr align="center">
<td><img src="images/polynomial-example.svg" alt="polynomial 4xy^2+3x-5" /></td>
</tr>
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<td>example of a polynomial<br />
this one has 3 terms</td>
</tr>
</table>
</div>
<h2>Dividing</h2>
<p>Sometimes it is easy to divide a polynomial by splitting it at the &quot;+&quot; and &quot;&minus;&quot; signs, like this (press play):</p>
<script type="text/javascript">playerMain("images/polynomials-dividing-a.txt",600,160);</script>
<p>When the polynomial was split into two parts we still had to keep the &quot;/3&quot; under each one.</p>
<p>Then the highlighted parts were &quot;reduced&quot; (<span class="frac"><sup>6</sup>/<sub>3</sub></span><b> = 2</b> and <span class="frac"><sup>3</sup>/<sub>3</sub></span><b> = 1</b>) to leave the answer of <b>2x-1</b></p>
<p>Here is another, slightly more complicated, example:</p>
<script type="text/javascript">playerMain("images/polynomials-dividing-b.txt",600,210);</script>
<p><i>What happened?</i> </p>
<ul>
<li>The 1st Term had <b>x<sup>2</sup></b> above and <b>x</b> below, which together becomes just <b>x</b></li>
<li>The 2nd Term had <b>x</b> above and below, so they canceled each other out</li>
<li>We couldn't simplify &quot;<span class="frac"><sup>1</sup>/<sub>3x</sub></span>&quot; any further. </li>
</ul>
<p>That is as far as we can get. But the answer is still &quot;simpler&quot;</p>
<p>Note: the result is a valid answer but is <b>not</b> a polynomial, because the last term (1/3x) has division by a variable (x).</p>
<p>&nbsp;</p>
<p>Now, sometimes it helps to rearrange the top polynomial before dividing, as in this example:</p>
<script type="text/javascript">playerMain("images/polynomials-dividing-c.txt",600,160);</script>
<h2>Long Division </h2>
<p>If none of those methods work, we may need to use <a href="polynomials-division-long.html">Polynomial Long Division</a>.</p>
<p>&nbsp;</p>
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<div class="related"> <a href="polynomials.html">Polynomials</a> <a href="introduction.html">Introduction to Algebra</a> <a href="definitions.html">Algebra - Basic Definitions</a> <a href="index.html">Algebra Index</a> </div>
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