Answer:
3x^4 - 3x^3 - 24x^2 + 120x - 96
Explanation:
When we approach one of these problems, we should try to write out an equation as if it were factored.
f(x) = a(x-1)(x+4)(x-2+2i)(x-2-2i)
note here that a is a constant we can solve for later. and I added the last root on since whenever we have 1 complex root, it's conjugate is also a complex root.
expanding this we obtain
f(x) = a(x^4 - x^3 - 8x^2 + 40x - 32)
we want f(0) = -96
what value of a would make the term with no variable attached equal to -96?
-32 × 3 = -96
so a =3 and our final answer is
3x^4 - 3x^3 - 24x^2 + 120x - 96