因式分解 (x+1)(x+2)(x+5)(x+7)+15
问题描述：
因式分解 (x+1)(x+2)(x+5)(x+7)+15
答
(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
=(x^2+8x+7)[(x^2+8x+7)+8]+15
=(x^2+8x+7)^2+8(x^2+8x+7)+15
=[(x^2+8x+7)+3][(x^2+8x+7)+5]
=(x^2+8x+10)(x^2+8x+12)
=(x^2+8x+10)(x+2)(x+6)
=(x+4-2根号6）（x+4+2根号6）（x+2)(x+6)