Answer
$P(x)=x^3(x-3)(x+3)$
Zeros: $-3, 0,\text{ and } 3$
Refer to the graph below.
Work Step by Step
Factor the polynomial completely to obtain:
\begin{align*}
P(x)&=x^3(x^2-9)\\
&=x^3(x-3)(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^3&=0 &\text{or}& &x-3=0& &\text{or}& &x+3=0\\
x&=0 &\text{or}& &x=3& &\text{or}& &x=-3\\
\end{align*}
Use a graphing utility to graph $P(x)$.
Refer to the graph above.
