Question

因式分解：(x^2+3x+2)(4x^2+8x+3)-90用换元法

Answer 1

(x^2+3x+2)(4x^2+8x+3)-90

=(x+2)(x+1)(2x+1)(2x+3)-90

=(x+2)(2x+1)(x+1)(2x+3)-90

=(2x^2+5x+2)(2x^2+5x+3)-90

令t=2x^2+5x

原式=(t+2)(t+3)-90

=(t+2)(t+2+1)-90

=(t+2)^2+(t+2)-90

=(t+2+10)(t+2-9)

=(t+12)(t-7)

=(2x^2+5x+12)(2x^2+5x-7)

=(2x^2+5x+12)(2x+7)(x-1)