Question

一道高中因式分解竞赛题x的5次方+1-x

Answer 1

x^5+1-x

=x^5+x^4-x^4+x^3-x^3+x^3+x^2-x^2+1-x

=x^4(1-x)+x^3(1-x)+x^2(1-x)+x(1-x)+1

=x^4(1-x)+x^3(1-x)+x^2(1-x)+x(1-x)+x^0*(1-x)

=(1-x)*(x^4+x^3+x^2+x^1+x^0)

=(1-x)*[1*(1-x^4)/(1-x)]

=1*(1-x^4)