chap7-summary.xml

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<section xml:id="chap7-summary" xmlns:xi="http://www.w3.org/2001/XInclude">
<title>Chapter Summary and Review</title>
<subsection><title>Key Concepts</title>
<p>
	<ol label="1">
		<li><p>The degree of a product of nonzero polynomials is the sum of the degrees of the factors.</p></li>
		<li><p>
			<xref ref="assemblage-cube-of-binomial"><term>Cube of a Binomial</term></xref>
		</p></li>
		<li><p><xref ref="assemblage-factoring-sum-of-cubes">Factoring the Sum or Difference of Two Cubes</xref></p></li>
		<li><p>The graphs of all polynomials are smooth curves without breaks or holes.</p></li>
		<li><p>The graph of a polynomial of degree <m>n</m> (with positive lead coefficient) has the same long-term behavior as the power function of the same degree.</p></li>
		<li><p><xref ref="assemblage-factor-theorem">Factor Theorem</xref></p></li>
		<li><p>A polynomial of degree <m>n</m> can have at most <m>n</m> <m>x</m>-intercepts.</p></li>
		<li><p>At a zero of multiplicity <m>2</m>, the graph of a polynomial has a turning point. At a zero of multiplicity <m>3</m>, the graph of a polynomial has an inflection point.</p></li>
		<li><p>The square root of a negative number is an imaginary number.</p></li>
		<li><p>A complex number is the sum of a real number and an imaginary number.</p></li>
		<li><p>We can perform the four arithmetic operations on complex numbers</p></li>
		<li><p>The product of a nonzero complex number and its conjugate is always a positive real number.</p></li>
		<li><p>
			<xref ref="assemblage-fundamental-theorem-of-algebra">The Fundamental theorem of algebra</xref>
		</p></li>
		<li><p>We can graph complex numbers in the complex plane</p></li>
		<li><p>Multiplying a complex number by <m>i</m> rotates its graph by <m>90\degree</m> around the origin.</p></li>
		<li><p>
			<xref ref="assemblage-rational-function">Rational function</xref>
		</p></li>
		<li><p>A rational function <m>f (x) = \frac{P(x)}{Q(x)}</m> is undefined for any value <m>x=a</m> where <m>Q(a) = 0</m>. These <m>x</m>-values are not in the domain of the function.</p></li>
		<li><p>
			<xref ref="assemblage-vertical-asymptotes">Vertical Asymptotes</xref>
		</p></li>
		<li><p>
			<xref ref="assemblage-horizontal-asymptotes">Horizontal Asymptotes</xref>
		</p></li>
		<li><p>To solve an equation involving an algebraic fraction, we multiply each side of the equation by the denominator of the fraction. This has the effect of clearing the fraction, giving us an equivalent equation without fractions.</p></li>
		<li><p>Whenever we multiply an equation by an expression containing the variable, we should check that the solutions obtained are not extraneous.</p></li>
	</ol>.
</p>
</subsection>
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</section>
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