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

x^5+x-1

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)