how do i solve this?

Question

Given that -1 is a zero of f(x)= x^4 + 5x^3 -4x^2-16x-8, find the remaining zeros.

Answer 1

-1 is a root of a polynomial if and only if x+1 divides the polynomial.

So divide f(x) by x+1.

You get g(x) = x^3 + 4x^2 - 8x -8.

By the Rational Root Theorem, the first candidates for being roots are +/- 1 and +/- 2. Except there can't be an odd root, so go straight to x = 2. That turns out to be a root also, so x-2 also divides g(x) (and f(x), of course).

Divide that into g(x), and you get x^2 +6x + 4. Solve that using the Quadratic Formula.

But better check all that; I did it completely in my head. ;)