Question

How do you find the quotient of `(h^3+2h^2-3h+9)/(h+3)` using synthetic division?

Answer 1

The remainder is `9` and the quotient is `=h^2-h`

Explanation:

Let's perform the synthetic division

`color(white)(aaaa)` `-3` `|` `color(white)(aaaa)` `1` `color(white)(aaaaa)` `2` `color(white)(aaaaaa)` `-3` `color(white)(aaaaaaa)` `9`

`color(white)(aaaaaaa)` ###|#`color(white)(aaaa)` ###color(white)(aaaa)#`-3` `color(white)(aaaaaaa)` `3` `color(white)(aaaaaaa)` `0`

`color(white)(aaaaaaaaa)` #`_________________________________________________________`#

`color(white)(aaaaaaa)` ###|#`color(white)(aaaa)` `1` `color(white)(aaa)` `-1` `color(white)(aaaaaaa)` `0` `color(white)(aaaaaaa)` `color(red)(9)`

The remainder is `9` and the quotient is `=h^2-h`

Therefore,

`(h^3+2h^2-3h+9)/(h+3)=(h^2-h)+9/(h+3)`