Question

How do you divide `(x^4+9)div(x+3)` using synthetic division?

Answer 1

The remainder is `color(red)(90)` and the quotient is `=x^3-3x^2+9x-27`

Explanation:

Let's perform the synthetic division

`color(white)(aa)` `-3` `color(white)(aaaaa)` `|` `color(white)(aaa)` `1` `color(white)(aaaaaaaa)` `0` `color(white)(aaaaaa)` `0` `color(white)(aaaaaaa)` `0` `color(white)(aaaaaa)` `9`
`color(white)(aaaaaaaaaaaa)` `------------`

`color(white)(aaaa)` `color(white)(aaaaaa)` `|` `color(white)(aaaaa)` `color(white)(aaaaa)` `-3` `color(white)(aaaaaa)` `9` `color(white)(aaaaa)` `-27` `color(white)(aaaaa)` `81`
`color(white)(aaaaaaaaaaaa)` `------------`

`color(white)(aaaa)` `color(white)(aaaaaa)` `|` `color(white)(aaa)` `1` `color(white)(aaaaaa)` `-3` `color(white)(aaaaaa)` `9` `color(white)(aaaaa)` `-27` `color(white)(aaaaa)` `color(red)(90)`

The remainder is `color(red)(90)` and the quotient is `=x^3-3x^2+9x-27`

`(x^4+9)/(x+3)=x^3-3x^2+9x-27+90/(x+3)`