X^3-12X+16=0怎样因式分解成(X-2)^2(X+4)=0这类题一般怎么入手？

x^3-12x+16=0
x^3+(-2x^2+2x^2)-12x+16=0
(x^3-2x^2)+(2x^2-12x+16)=0
x^2(x-2)+2(x^2-6x+8)=0
x^2(x-2)+2(x-2)(x-4)=0
(x-2)(x^2+2x-8)=0
(x-2)(x+4)(x-2)=0
(x-2)^2(x+4)=0

x^3-12X+16=0
x^3-2x^2+2x^2-4x-8x+16=0
x^2(x-2)+2x(x-2)-8(x-2)=0
(x-2)(x^2+2x-8)=0
(x-2)(x+4)(x-2)=0
(x-2)^2(x+4)=0

原式=x³-4x-8x+16
=x(x²-4)-8(x-2)
=x(x+2)(x-2)-8(x-2)
=(x-2)(x²+2x-8)
=(x-2)(x+4)(x-2)
=(x-2)²(x+4)