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: 33

Answer

$P(x)=-x(x-4)(x+3)$ Zeros: $-3, 0, \text{ and } 4$ Refer to the graph below.
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Work Step by Step

Factor the polynomial completely to obtain: \begin{align*} P(x)&=-x(x^2-x-12)\\ &=-x(x-4)(x+3) \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-4=0& &\text{or}& &x+3=0\\ x&=0 &\text{or}& &x=4& &\text{or}& &x=-3 \end{align*} Use a graphing utility to graph $P(x)$. Refer to the graph above.
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