(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)