`\qquad (x^8+x^4+1):(x^2+x+1)`
`=(x^8-x^2+x^4-x+x^2+x+1):(x^2+x+1)`
`=[x^2(x^6-1)+x(x^3-1)+(x^2+x+1)]:(x^2+x+1)`
`=[x^2(x^3-1)(x^3+1)+x(x-1)(x^2+x+1)+(x^2+x+1)]:(x^2+x+1)`
`=[(x-1)(x^2+x+1)(x^5+x^2)+(x^2+x+1)(x^2-x)+(x^2+x+1)]:(x^2+x+1)`
`=(x^2+x+1)[(x-1)(x^5+x^2)+x^2-x+1]:(x^2+x+1)`
`=x^6+x^3-x^5-x^2+x^2-x+1`
`=x^6-x^5+x^3-x+1`