分解因式:(x+1)(x+2)(x+3)(x+4)-120=_.
问题描述:
分解因式:(x+1)(x+2)(x+3)(x+4)-120=______.
答
(x+1)(x+2)(x+3)(x+4)-120
=(x2+5x+6)(x2+5x+4)-120
=(x2+5x)2+10(x2+5x)+24-120
=(x2+5x)2+10(x2+5x)-96
=(x2+5x+16)(x2+5x-6)
=(x2+5x+16)(x+6)(x-1).