Answer
zeros: $0$ and $-4$
$x$-intercepts: $0$ and $-4$
Work Step by Step
Factor the polynomial to obtain:
$$f(x) = x(x+4)$$
Set $f(x) =0$ to obtain:
$$0=x(x+4)$$
Find the zeros of the function by solving the equation above using the Zero Product Property to obtain:
\begin{align*}
x&=0 &\text{ or }& &x+4=0\\
x&=0 &\text{ or }& &x=-4\end{align*}
The zeros are $0$ and $-4$.
The $x$-intercepts are $0$ and $-4$.
