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.
