Question

How do you use long division to divide `(x^3-9)div(x^2+1)`?

Answer 1

The quotient is `x` and the remainder is `=-(x+9)`

Explanation:

Let's perform the long division

`color(white)(aaaa)` `x^2+1` `color(white)(aaaa)` `|` `x^3` `color(white)(aaaa)` `+0x^2` `color(white)(aaaa)` `+0x` `color(white)(aaaa)` `-9` `color(white)(aaaa)` `|` `x`

`color(white)(aaaa)` `color(white)(aaaaaaaaaaa)` `x^3` `color(white)(aaaa)` `color(white)(aaaaaaaaa)` `+x` `color(white)(aaaa)`

`color(white)(aaaa)` `color(white)(aaaaaaaaaaa)` `0` `color(white)(aaaa)` `color(white)(aaaaaaaaaa)` `-x` `color(white)(aaaa)` `-9`

The quotient is `x` and the remainder is `=-(x+9)`

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