因式分解：x^4+x^3-2x^2-x+1

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因式分解：x^4+x^3-2x^2-x+1
因式分解：x^4+x^3-2x^2-x+1

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

答：
x^4+x^3-2x^2-x+1
=(x^2+x-2)x^2-(x-1)
=(x-1)(x+2)x^2-(x-1)
=(x-1)(x^3+2x^2-1)
=(x-1)(x^3+x^2+x^2-1)
=(x-1)(x+1)(x^2+x-1)

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

原式=(x^4-2x^2+1)+(x^3-x)
=(x^2-1)^2+x(x^2-1)
=(x^2-1)(x^2+x-1)
=(x+1)(x-1)(x^2+x-1)

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