(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)