Question

How do you divide `(6b^3+28b^2+25b-21)div(b+3)` using synthetic division?

Answer 1

The quotient is `=6b^2+10b-5` and the remainder is `=-6`

Explanation:

We perform the synthetic division

`color(white)(aaaa)` `-3` `color(white)(aaaa)` `|` `color(white)(aaaa)` `6` `color(white)(aaaa)` `28` `color(white)(aaaaa)` `25` `color(white)(aaa)` `-21`

`color(white)(aaaaaa)` `color(white)(aaaaa)` `|` `color(white)(aaaaa)` `color(white)(aa)` `-18` `color(white)(aaaa)` `-30` `color(white)(aaaa)` `15`

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

`color(white)(aaaa)` `color(white)(aaaaaa)` `color(white)(aaaaaa)` `6` `color(white)(aaaa)` `10` `color(white)(aaaa)` `-5` `color(white)(aaaa)` `color(red)(-6)`

The remainder is `=-6`

The quotient is `=6b^2+10b-5`