Question

How do you divide `x^5+x^3+x` by `x^2+x+1` ?

Answer 1

`(x^5+x^3+x)/(x^2+x+1) = x^3-x^2+x`

Explanation:

`(x^5+x^3+x)/(x^2+x+1) = ((x^5+x^4+x^3)-(x^4+x^3+x^2)+(x^3+x^2+x))/(x^2+x+1)`

`color(white)((x^5+x^3+x)/(x^2+x+1)) = ((x^3-x^2+x)color(red)(cancel(color(black)((x^2+x+1)))))/color(red)(cancel(color(black)((x^2+x+1))))`

`color(white)((x^5+x^3+x)/(x^2+x+1)) = x^3-x^2+x`