Question

How do you divide `(m^3-13m^2+24m+18)div(m-3)` using synthetic division?

Answer 1

The remainder is `=0`
The quotient is `=m^2-10m-6`

Explanation:

We perform a synthetic division

`color(white)(aaaa)` `3` `color(white)(aaaa)` `|` `color(white)(aaaa)` `1` `color(white)(aaaa)` `-13` `color(white)(aaaaaaa)` `24` `color(white)(aaaaaa)` `18` `color(white)(aaaaaa)`##

`color(white)(aaaaaa)` `color(white)(aaa)` `|` `color(white)(aaa)` `color(white)(aaaaaaaaa)` `3` `color(white)(aaaaa)` `-30` `color(white)(aaaa)` `-18` `color(white)(aaaaaa)`##

`color(white)(aaaaaaaaaa)`------------------------------------------------------------

`color(white)(aaaa)color(white)(aaaaaa)color(white)(aaaaaa)1color(white)(aaaa)-10` `color(white)(aaaaa)-6color(white)(aaaaa)color(white)(aa)color(red)(0)`

The remainder is `=0`

The quotient is `=m^2-10m-6`