因式分解(x²+3x+2)(x²+7x+12)-120
问题描述：
因式分解(x²+3x+2)(x²+7x+12)-120
答
(x^2+3x+2)(x^2+7x+12)-120
=(x+1)(x+2)(x+3)(x+4)-120
=(x+1)(x+4)(x+2)(x+3)-120
=(x^2+5x+4)(x^2+5x+6)-120
设y=x^2+5x+5
原式
=(y-1)(y+1)-120
=y^2-1-120
=y^2-121
=(y+11)(y-11)
=(x^2+5x+16)(x^2+5x-6)
=(x^2+5x+16)(x-1)(x+6)