# Chapter 3, Polynomial and Rational Functions - Section 3.2 - Polynomial Functions and Their Graphs - 3.2 Exercises - Page 302: 32

$P(x)=x(x+4)(x-2)$ Zeros: $-4, 0, \text{ and }2$ Refer to the graph below.

#### Work Step by Step

Factor the polynomial completely to obtain: \begin{align*} P(x)&=x(x^2+2x-8)\\ &=x(x+4)(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+4=0& &\text{or}& &x-2=0\\ x&=0 &\text{or}& &x=-4& &\text{or}& &x=2 \end{align*} Use a graphing utility to graph $P(x)$. Refer to the graph above.

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