#### Answer

$x^4-3x^3-15x^2+19x +30$

#### Work Step by Step

Let us consider that $a$ is a zero of the function with multiplicity $b$. Then this factor of the function can be expressed as: $(x-a)^b$.
We are given that the degree is $4$, and the zeros are $-3$, $-1$, $2$, and $5$.
Therefore, we can write the equation of the function as:
$f(x)=(x+3)(x+1)(x-2)(x-5) \\=x^4-3x^3-15x^2+19x +30$