因式分解：x的5次方-x+1

Question

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

Answer 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)本回答被提问者采纳

Answer 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)

Answer 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)

Answer 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)