因式分解：x(x-1)(x-2)(x-3)-24
问题描述：
因式分解：x(x-1)(x-2)(x-3)-24
答
x(x-1)(x-2)(x-3)-24
=[x(x-3)][(x-1)(x-2)]-24
=(x²-3x)(x²-3x+2)-24
=(x²-3x)²+2(x²-3x)-24
=[(x²-3x)+6][(x²-3x)-4]
=(x²-3x+6)(x²-3x-4)
=(x²-3x+6)(x-4)(x+1)