Question

因式分解(x^2+4x+3)(x^2+12x+35)+15

Answer 1

(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)