因式分解：x的5次方-x+1

因式分解：x的5次方-x+1对不起，打错了，是 x的5次方+x-1

2024-12-26 22:18:05

推荐回答（4个）

回答1：

因式分解：x^5+x-1

解：
x^5+x-1
=(x^5+x^2)-(x^2-x+1)
=x^2(x^3+1)-(x^2-x+1)
=x^2(x+1)(x^2-x+1)-(x^2-x+1)
=(x^2-x+1)[x^2(x+1)-1]
=(x^2-x+1)(x^3+x^2-1)

回答2：

x^5+x-1
=x^5+x^2-x^2+x-1
=x^2(x^3+1)-(x^2-x+1)
=x^2(x+1)(x^2-x+1)-(x^2-x+1)
=(x^2-x+1)[x^2(x+1)-1]
=(x^2-x+1)(x^3+x^2-1)

回答3：

解： x^5+x-1
=(x^5+x^2)-(x^2-x+1)
=x^2(x^3+1)-(x^2-x+1)
=x^2(x+1)(x^2-x+1)-(x^2-x+1)
=(x^2-x+1)[x^2(x+1)-1]
=(x^2-x+1)(x^3+x^2-1)

回答4：

x^5+x-1
原式=(x^5+x^2)-(x^2-x+1)
=x^2(x^3+1)-(x^2-x+1)
=x^2(x+1)(x^2-x+1)-(x^2-x+1)
=(x^2-x+1)[x^2(x+1)-1]
=(x^2-x+1)(x^3+x^2-1)