x的五次方-3x的四次方-x的三次方+11x的二次方-12x+4
问题描述：
x的五次方-3x的四次方-x的三次方+11x的二次方-12x+4
答
原式=x^5-x^4-2x^4+2x³-3x³+3x²+8x²-8x-4x+4
=x^4(x-1)-2x³(x-1)-3x²(x-1)+8x(x-1)-4(x-1)
=(x-1)(x^4-2x³-3x²+8x-4)
=(x-1)(x^4-x³-x³+x²-4x²+4x+4x-4)
=(x-1)[x³(x-1)-x²(x-1)-4x(x-1)+4(x-1)]
=(x-1)²(x³-x²-4x+4)
=(x-1)²[x²(x-1)-4(x-1)]
=(x-1)³(x²-4)
=(x-1)³(x+2)(x-2)