Answer
$x^3+2x^2-8x$
Work Step by Step
Let us consider that $a$ is a zero of the function with multiplicity $b$. Then the factor of the function can be expressed as: $(x-a)^b$.
We are given that the degree is $3$, and the zeros are $-4$, $0$ and $2$.
Therefore, we can write the equation of the function as:
$f(x)=a(x+4)(x-0)(x-2)\\=a(x^3+2x^2-8x)$
When $a=1$, the function can be written as:
$f(x)=x^3+2x^2-8x$
