Answer
$P(x)=-x(2x-1)(x+1)$
Zeros: $-1, 0, \text{ and } \dfrac{1}{2}$
Refer to the graph below.
Work Step by Step
Factor the polynomial completely to obtain:
\begin{align*}
P(x)&=-x(2x^2+x-1)\\
&=-x(2x-1)(x+1)
\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}& &2x-1=0& &\text{or}& &x+1=0\\
x&=0 &\text{or}& &2x=1& &\text{or}& &x=-1\\
x&=0 &\text{or}& &x=\frac{1}{2}& &\text{or}& &x=-1\\
\end{align*}
Use a graphing utility to graph $P(x)$.
Refer to the graph above.
