Answer
$P(x)=(x-2)(x+2)(x^2+1)$
Zeros: $-2$ and $2$.
Refer to the graph below.
Work Step by Step
Factor the polynomial completely to obtain:
\begin{align*}
P(x)&=(x^2-4)(x^2+1)\\
&=(x-2)(x+2)(x^2+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^2+1=0\\
x&=2 &\text{or}& &x=-2& &\text{or}& &\text{(no real solution)} \\
\end{align*}
The zeros of the function are $-2$ and $2$.
Use a graphing utility to graph P(x).
Refer to the graph above.
