Question

分解因式 （x²+3x+2）*（x²+7x+12）—120

Answer 1

(x²+3x+2)*(x²+7x+12)-120
=(x+1)(x+2)(x+3)(x+4)-120
=(x+1)(x+4)(x+2)(x+3)-120
=(x²+5x+4)(x²+5x+6)-120
=(x²+5x+4)[(x²+5x+4)+2]-120
=(x²+5x+4)²+2(x²+5x+4)-120
=(x²+5x+4+12)(x²+5x+4-10)
=(x²+5x+16)(x²+5x-6)
=(x²+5x+16)(x+6)(x-1)

Answer 2

原式=（x+1)*(x+2)*（x+4）*（x+3）-120
=（x+1)*(x+4）*(x+2）*（x+3）-120
=（x*x+5x+4）*(x*x+5x+6)-120
=（x*x+5x)*（x*x+5x)+10*(x*x+5x)+24-120
=（x*x+5x)*（x*x+5x)+10*(x*x+5x)-96
=（x*x+5x-6)(x*x+5x+16)
=(x-1)(x+6)(x*x+5x+16)
完成