Answer
$P(x)=x(x+4)(x-2)$
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.
