（x-1)(x-2)(x-3)(x-4)-120 化简的,

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（x-1)(x-2)(x-3)(x-4)-120化简的,（x-1)(x-2)(x-3)(x-4)-120化简的,（x-1)(x-2)(x-3)(x-4)-120化简的,（x-1)(x-2)(x-3)(

（x-1)(x-2)(x-3)(x-4)-120 化简的,
（x-1)(x-2)(x-3)(x-4)-120 化简的,

（x-1)(x-2)(x-3)(x-4)-120 化简的,
（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)

（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)²+2(x²-5x+6)-120
=(x²-5x+4)²+2(x²-5x+6)+1-120-1
=(x²-5x+4+1)²-121
=(x²-5x+5+11)(x²-5x+5-11)
=(x²-5x+16)(x²-5x-6)
=(x+1)(x-6)(x²-5x+16)

观察（x-1)(x-2)(x-3)(x-4)-120，(x-1)(x-4)和(x-2)(x-3)有相同的最高次项和次高项，因此：
（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
...

全部展开

观察（x-1)(x-2)(x-3)(x-4)-120，(x-1)(x-4)和(x-2)(x-3)有相同的最高次项和次高项，因此：
（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)^2+10(x^2-5x)-16*6
=[(x^2-5x)+16][(x^2-5x)-6]
=(x^2-5x+16)(x^2-5x-6)
=(x^2-5x+16)(x-6)(x+1)

收起

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