Question

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

Answer 1

The answer is `=2x^2-2x+3`

Explanation:

You can do a long division

`color(white)(aaaa)` `2x^3` `color(white)(aaaaaaa)` `x+3` `color(white)(aaaaa)` `|` `x+1`

`color(white)(aaaa)` `2x^3+2x^2` `color(white)(aaaa)` ###color(white)(aaaaaaaa)#`|` `2x^2-2x+3`

`color(white)(aaaaa)` `0-2x^2+x`

`color(white)(aaaaaaa)` `-2x^2-2x`

`color(white)(aaaaaaaa)` `-0+3x+3`

`color(white)(aaaaaaaaaaaa)` `+3x+3`

`color(white)(aaaaaaaaaaaaa)` `+0+0`

Therefore,

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