用换元法分解因式(x^2+4x+3)(x^2+12x+35)+15

2024-12-15 18:49:27
推荐回答(2个)
回答1:

(x^2+4x+3)(x^2+12x+35)+15
=(x+1)(x+3)(x+5)(x+7)+15
=(x^2+8x+7)(x^2+8x+15)+15
设t=x^2+8x+11,
上式=(t-4)(t+4)+15
=t^2-16+15
=(t-1)(t+1)
=(x^2+8x+10)(x^2+8x+12)
=(x+4+√6)(x+4-√6)(x+2)(x+6).

回答2:

设Y=x+2,z=x+3

原式变为

(y^2-1)(z^2-1)+15
=(y+1)(y-1)(z+1)(z-1)+15