求分解因式：x^4+2x^3-2x^2-2x+1
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求分解因式：x^4+2x^3-2x^2-2x+1
求分解因式：x^4+2x^3-2x^2-2x+1
求分解因式：x^4+2x^3-2x^2-2x+1
x^4+2x^3-2x^2-2x+1=x^4+2x^3-3x^2+x^2-2x+1=x^2(x+3)(x-1)+(x-1)^2=(x-1)(x^3+3x^2+x-1)=(x+1)(x-1)(x^2+2x-1)
方法1：原式=x^4+2x^3+x^2-2x^2-2x+1
=(x(x+1))^2-2x(x+1)+1
=(x(x+1)-1)^2
=(x^2+x-1)^2
方法2:原式==x^4+x^3-2x^2-2x+x^3+1
=x^3(x+1)-2x(x+1)+(x+1)(x^2-x+1)
=(x+1)(x^3-2x+x^2-x+1)
=(x+...
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方法1：原式=x^4+2x^3+x^2-2x^2-2x+1
=(x(x+1))^2-2x(x+1)+1
=(x(x+1)-1)^2
=(x^2+x-1)^2
方法2:原式==x^4+x^3-2x^2-2x+x^3+1
=x^3(x+1)-2x(x+1)+(x+1)(x^2-x+1)
=(x+1)(x^3-2x+x^2-x+1)
=(x+1)(x^3+x^2-3x+1)
=(x+1)(x³-x+x²-2x+1)
=(x+1)[x(x-1)(x+1)+(x-1)²]
=(x+1)(x-1)(x²+x+x-1)
=(x+1)(x-1)(x²+2x-1)
两种方法结果不同，但算出来都符合你所给的条件，望采纳。祝你学习上有所进步！！
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x^4+2x^3-2x^2-2x+1
=x^4+x^3-2x^2-2x+x^3+1
=x^3(x+1)-2x(x+1)+(x+1)(x^2-x+1)
=(x+1)(x^3-2x+x^2-x+1)
=(x+1)(x^3+x^2-3x+1)
(x^2+x-1)^2
原式=（x+1)(x^3+3x^2+x+1)
x^4+2x^3-2x^2-2x+1
=x^4+2x^3+x²-3x²-2x+1
=x²(x²+2x+1)-(3x²+2x-1)
=x²(x+1)²-(3x-1)(x+1)
=(x+1)(x³+x²-3x+1)
=(x+1)(x³-x+x²-2x+1)
=(x+1)[x(x-1)(x+1)+(x-1)²]
=(x+1)(x-1)(x²+x+x-1)
=(x+1)(x-1)(x²+2x-1)