Factor the expression completely over the complex numbers.

x^3-4x^2+4x-16

First you must know that is i∧2 = - 1

x∧3-4x∧2+4x-16 = x∧2 (x-4) + 4 (x-4) = (x-4) (x∧2+4) = (x-4) (x∧2 - (-4)) =

= (x-4) (x∧2 - (-1) * 4) = (x-4) (x∧2 - i∧2*2∧2) = (x-4) (x∧2 - (2i) ∧2) = (x-4) (x-2i) (x+2i)

Good luck!