用换元法分解因式(x^2+4x+3)(x^2+12x+35)+15
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用换元法分解因式(x^2+4x+3)(x^2+12x+35)+15
![用换元法分解因式(x^2+4x+3)(x^2+12x+35)+15](/uploads/image/z/17501485-13-5.jpg?t=%E7%94%A8%E6%8D%A2%E5%85%83%E6%B3%95%E5%88%86%E8%A7%A3%E5%9B%A0%E5%BC%8F%28x%5E2%2B4x%2B3%29%28x%5E2%2B12x%2B35%29%2B15)
(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).
=(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).