Answer
$P(x)=x^2(x-2)9x-1)$
Zeros: $0$ multiplicity $2$, $1$, and $2$
Refer to teg graph below.
Work Step by Step
Factor the polynomial completely to obtain:
\begin{align*}
P(x)&=x^2(x^2-3x+2)\\
&=x^2(x-2)(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^2&=0 &\text{or}& &x-2=0& &\text{or}& &x-1=0\\
x&=\pm0 &\text{or}& &x=2& &\text{or}& &x=1\\
x&=0 \text{ (multiplicity 2)} &\text{or}& &x=2& &\text{or}& &x=1\\
\end{align*}
Use a graphing utility to graph $P(x)$.
Refer to the graph above.
