<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="description">
    <name>
      <text>1.2.3.1 Polynomial expressions</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<h3>Polynomial expressions
</h3>
<p>An important group of mathematical expressions which use indices are known as <b>polynomials</b>.</p>

<p>Examples of polynomials are</p>
<ul>
    <li> \(4x^3+2x^2+3x-7\),</li>
    <li>\( x^2+x \), </li>
    <li>\( 17-2t+7t^4 \), </li>
    <li>\( z-z^3 \). </li>
</ul>

<p>Notice that they are all constructed using non-negative whole number powers of the variable. Recall that \(x^0=1\) and so the number \(-7\) appearing in the first expression can be thought of as \(-7x^0\). Similarly the \(17\) appearing in the third expression
    can be read as \(17t^0\).<br><br></p>


<div class="HELM_keypoint">
    <h4>Key Point <br></h4>
    <p>A polynomial expression takes the form</p>
    <p>\( a_0 + a_1x + a_2x^2 + a_3x^3 +\ldots + a_nx^n\)</p>
    <p>where \( a_0 ,a_1, a_2, a_3, \ldots a_n\) are all constants called the <b>coefficients</b> of the polynomial. The number \(a_0\) is also called the <b>constant term</b>. The highest power in a polynomial is called the <b>degree</b> of the polynomial.</p>
    <p>Polynomials with low degrees have special names and subscript notation is often not needed:
    </p>
    <table>
        <thead>
            <tr>
                <th style="min-width:12em">Polynomial</th>
                <th style="min-width:5em">Degree</th>
                <th style="min-width:7em">Name</th>
            </tr>
        </thead>
        <tbody>
            <tr>
                <td style="text-align:center">\[ ax^3+bx^2+cx+d \]</td>
                <td style="text-align:center">3</td>
                <td style="text-align:center">cubic</td>
            </tr>
            <tr>
                <td style="text-align:center">\[ ax^2+bx+c \]</td>
                <td style="text-align:center">2</td>
                <td style="text-align:center">quadratic</td>
            </tr>
            <tr>
                <td style="text-align:center">\[ ax+b \]</td>
                <td style="text-align:center">1</td>
                <td style="text-align:center">linear</td>
            </tr>
            <tr>
                <td style="text-align:center">\[ a\]</td>
                <td style="text-align:center">0</td>
                <td style="text-align:center">constant</td>
            </tr>
        </tbody>
    </table>
</div>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text/>
    </generalfeedback>
    <defaultgrade>0</defaultgrade>
    <penalty>0</penalty>
    <hidden>0</hidden>
    <idnumber/>
  </question>
</quiz>
