因式分解：(X-1)(X-2)(X-3)(X-4)-120(x-1)(x-2)(x-3)(x-4)-120

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因式分解：(X-1)(X-2)(X-3)(X-4)-120(x-1)(x-2)(x-3)(x-4)-120

因式分解：(X-1)(X-2)(X-3)(X-4)-120(x-1)(x-2)(x-3)(x-4)-120
因式分解：(X-1)(X-2)(X-3)(X-4)-120
(x-1)(x-2)(x-3)(x-4)-120

因式分解：(X-1)(X-2)(X-3)(X-4)-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)+24-120
=(X²-5X)²+10(X²-5X)-96
=(X²-5X-6)(X²-5X+16)
=(X-6)(X+1)(X²-5X+16)

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(x-1)(x-2)(x-3)(x-4)-120
=[(x-1)(x-4)][(x-2)(x-3)]-120
=[(x^2-5x)+4][(x^2-5x)+6]-120
=[x^2-5x]^2+10[x^2-5x]+24-120
=[x^2-5x]^2+10[x^2-5x]-96
=[x^2-5x+16][x^2-5x-6]
=[x^2-5x+16][x-6][x+1]

两项两项来，(x-1)(x-4)=x^2-5x+4,(x-2)(x-3)=x^2-5x+6,原式即为(x^2-5x+4)*(x^2-5x+6)-120=(x^2-5x)^2+10(x^2-5x)-96=(x^2-5x+16)*(x^2-5x-6)=(x^2-5x+16)*(x+1)*(x-6)

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