(x^2-2x+2)^2-11x^2+22x-12
=(x^2-2x+2)^2-11x^2+22x-22+10
=(x^2-2x+2)^2-11(x^2-2x+2)+10
=(x^2-2x+2-10)(x^2-2x+2-1)
=(x^2-2x-8)(x^2-2x+1)
=(x-4)(x+2)(x-1)^2