分解因式x^3-3(a+1)x+3a+2

x^3-3(a+1)x+3a+2
=x^3 - x^2 + x^2 - 3a*x -3x +3a +2
=(x^3 - x^2 -2x + 2 )+ (x^2 - 3a*x -x +3a)
=(x^2-2)(x-1) + (x-3a)(x-1)
=(x-1)(x^2+x-3a-2)

x^2-3(a+1)x+3a+2
=(x-3a-2)(x-1)

原题=x³-x²+x²-3(a+1)x+3a+2
=x²(x-1)+(x-3a-2)(x-1)
=(x-1)(x²+x-3a-2)
=(x-1)(x²+x+1/4-1/4-3a-2)
=(x-1){(x+1/4)²-[√(3a+9/4)]²}
=(x-1)[x+1/4+√(3a+9/4)][x+1/4-√(3a+9/4)]