因式分解：x^4+x^3-2x^2-x+1

x^4+x^3-2x^2-x+1
=(x^4-x^3)+(2x^3-2x^2)-(x-1)
=x^3(x-1)+2x^2(x-1)-(x-1)
=(x-1)(x^3+2x^2-1)
=(x-1)[(x^3+x^2+x^2-1)]
=(x-1)[x^2(x+1)+(x+1)(x-1)]
=(x-1)(x+1)(x^2+x-1) 有理数范围内
=(x-1)(x+1)[x-(√5-1)/2][x+(√5+1)/2] 实数范围内