Question

1+x+x^2+x^3+x^4=(1-x^5)/(1-x)这个因式分解的过程是怎样的?

Answer 1

由于 (1-x)（1+x+x^2）=1-x^3

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

=(1-x^3)/(1-x)+[x^3*(1+x)*(1-x)]/(1-x)

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

=(1-x^3)/(1-x)+(x^3-x^5))/(1-x)

=(1-x^3+x^3-x^5)/(1-x)

=(1-x^5)/(1-x)