(x^+3x+2)(x^+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)²+10(x²+5x)-96
=(x²+5x+16)(x²+5x-6)
=(x²+5x+16)(x+6)(x-1)