Answer
$f(x)=x^4+x^3+23x-10$
Work Step by Step
One of the zeroes must be a repeated zero so that we can find a polynomial of degree 3. Let's make $x=1$ a repeated zero:
$f(x)=a[x-(-5)](x-1)^2(x-2)=a(x+5)(x^2-2x+1)(x-2)=a(x^3+3x^2-9x+5)(x-2)=a(x^4+x^3+23x-10)$
$a$ can be any value. If $a=1$:
$f(x)=x^4+x^3+23x-10$
