Question

(x-1)(x-3)(x-5)(x-7)-84因式分解

Answer 1

(x-1)(x-3)(x-5)(x-7)-84
=[(x-1)(x-7)][(x-3)(x-5)]-84
=[(x²-8x)+7][(x²-8x)+15]-84
=(x²-8x)²+22(x²-8x)+105-84
=(x²-8x)²+22(x²-8x)+21
=[(x²-8x)+1][(x²-8x)+21]
=(x²-8x+1)(x²-8x+21)

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Answer 2

(x-1)(x-3)(x-5)(x-7)-84
=[(x-3)(x-5)][(x-1)(x-7)]-84
=(x²-8x+15)(x²-8x+7)-84
=(x²-8x)²+22(x²-8x)+105-84
=(x²-8x)²+22(x²-8x)+21
=(x²-8x+1)(x²-8x+21)

Answer 3

(x-1)(x-3)(x-5)(x-7)-84
=(x-1)(x-7)(x-3)(x-5)-84
=(x²-8x+7)(x²-8x+15)-84
=(x²-8x)²+22(x²-8x)+105-84
=(x²-8x)²+22(x²-8x)+21
=(x²-8x+1)(x²-8x+21)

Answer 4

(x-1)(x-3)(x-5)(x-7)-84
=[(x-1)(x-7)][(x-3)(x-5)]-84
=(x²-8x+7)(x²-8x+15)-84
令x²-8x=t
=(t+7)(t+15)-84
=t²+22t+21
=(t+1)(t+21)
=(x²-8x+1)(x²-8x+21)