Answer
$x^4-15x^2+10x +24$
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 $4$, and the zeros are $-4$, $-1$, $2$ and $3$.
Therefore, we can write the equation of the function as:
$f(x)=(x+4)(x+1)(x-2)(x-3) \\=x^4-15x^2+10x +24$