Question

How do you divide `(x^4+2x^3-2x^2+9x+3)/(x^2+1)`?

Answer 1

`x^2+2x-3+(7x+6)/(x^2+1)`

Explanation:

By long division

`(x^4+2x^3-2x^2+9x+3):(x^2+1)=x^2`
`-x^4-x^2`

`(0+2x^3-3x^2+9x+3):(x^2+1)=x^2+2x`
`-2x^3-2x`

`(0+0-3x^2+7x+3):(x^2+1)=x^2+2x-3`
`+3x^2+3`

`(0+0+0+7x+6):(x^2+1)=x^2+2x-3`

`x^2+2x-3+(7x+6)/(x^2+1)`