因式分解(x^2+4x+3)(x^2+12x+35)+15
问题描述：
因式分解(x^2+4x+3)(x^2+12x+35)+15
答
(x^2+4x+3)(x^2+12x+35)+15
=(x+1)(x+3)(x+5)(x+7)+15
=[(x+1)(x+7)][(x+3)(x+5)]+15
=(x^2+8x+7)(x^2+8x+15)+15
令K=x^2+8x+7
则
上式
=K(K+8)+15
=K^2+8K+15
=(K+3)(K+5)
=(x^2+8x+7+3)(x^2+8x+7+5)
=(x^2+8x+10)(x^2+8x+12)
=(x+2)(x+6)(x^2+8x+10)