Question

Use synthetic division to complete the indicated factorization.
x^4-4x^3-5x^2+36x-36=(x-3)(_)

Answer 1

So the problem I always had with synthetic division was I always had to guess what the roots are
But I'll give it a shot here
x^4-4x^3-5x^2+36x-36/(x-3)=x^3-x^2-8x+12
divide by x+3 and you get x^2-4x+4
and that gives (x-2)(x-2)
so the roots are 2, 2, 3, -3
or the factorization is (x-3)(x+3)(x-2)(x-2)