Question

请问如何解（x^2+3x+2)(x^2-9x+20)-72

Answer 1

另x^2-3x=y,原式(x^2+3x+2)(x^2-9x+20)-72=(y+6x+2)(y-6x+20)-72=y^2+22y+(-36x^2+108x)-32=y^2+22y-36y-32=y^2-14y-32=(y-16)(y+2)=(x^2-3x-16)(x^2-3x+2)=(x-1)(x-2)(x^2-3x-16).