#### Answer

$f(x)=x^4+10x^3+35x^2+50x+24$

#### Work Step by Step

RECALL:
If $a$ is a zero of a polynomial, then $x−a$ is a factor of the polynomial.
Thus, having $x=-1, -2, -3, -4$ as zeros of the polynomial function means that $x+1,x+2, x+3$, and $x+4$ are factors of the polynomial.
Therefore the function is
$f(x)=(x+1)(x+2)(x+3)(x+4)
\\f(x)=x^4+10x^3+35x^2+50x+24.$