College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 3, Polynomial and Rational Functions - Section 3.2 - Polynomial Functions and Their Graphs - 3.2 Exercises - Page 302: 31

Answer

$P(x)=x(x-3)(x+2)$ Zeros: $-2, 0, \text{ and } 3$ Refer to the graph below.

Work Step by Step

Factor the polynomial completely to obtain: \begin{align*} P(x)&=x(x^2-x-6)\\ &=x(x-3)(x+2) \end{align*} To find the zeros, use the Zero-Product Property by equating each factor to $0$, then solve each equation to obtain: \begin{align*} x&=0 &\text{or}& &x-3=0& &\text{or}& &x+2=0\\ x&=0 &\text{or}& &x=3& &\text{or}& &x=-2 \end{align*} Use a graphing utility to graph $P(x)$. Refer to the graph above.
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