$x^4 – 2x^3 – 2x^2 + 8x – 8$
$x^3 (x – 2) -2 (x^2 -4x +4)$
$x^3 (x – 2) -2(x-2)^2$
$(x-2)(x^3 – 2(x-2))$
$(x-2)(x^3 – 2x+4 +4 -4)$
$(x-2)(x^3 +8 -2x-4)$
$(x-2)(x^3 +2^3 -2(x+2))$
$(x-2)((x+2)(x^2 +4-2x) -2(x+2))$
$(x-2)(x+2)(x^2 -2x +2)$
$(x-2)(x+2)(x- (1\pm i))$