Question

因式分解 x的5次方+x+1 请详解

Answer 1

x^5+x+1=(x^5-x^2)+(x^2+x+1)（加一项减一项）=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^3-x^2+1)