(x-1)(x-3)(x-5)(x-7)-84因式分解
问题描述：
(x-1)(x-3)(x-5)(x-7)-84因式分解
答
(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)
答
(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)
答
(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]...
答
(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)