Answer
$f(x)=x^4+10x^3+33x^2+40x+16$
Work Step by Step
Make both zeroes repeated in order to get a polynomial of degree 4:
$f(x)=a[x-(-4)]^2[x-(-1)]^2=a(x^2+8x+16)(x^2+2x+1)=a(x^4+10x^3+33x^2+40x+16)$
$a$ can be any value. If $a=1$:
$f(x)=x^4+10x^3+33x^2+40x+16$
