Answer
$f(x)=x^3+2x^2-8x$
Work Step by Step
If $c$ is a zero of a function with multiplicity $b$ then $(x-c)^b$ is a “factor” of the function.
We are given that the degree is $3$, and the zeros are $-4$, $0$ and $2$, hence
$f(x)=a(x+4)(x)(x-2)=a(x^3+2x^2-8x)$
If $a=1$ the function is $f(x)=x^3+2x^2-8x$