Question

How do you divide `(r^3+6r^2-21r-18) div (r-3)` using synthetic division?

Answer 1

`=r^2+9r+6`

Explanation:

`(r^3+6r^2-21r-18)-:(r-3)`

`color(white)(aaaa)` `3|` # #
`color(white)(aaaaaaaaaaa)` `---------`
`color(white)(aaaaaaaaaaaa)`1`color(white)(aaaa)`6`color(white) (aaaa)`-21`color(white)(aaaa)`-18
`color(white)(aaaaaaaaaaaa)` `color(white)(aaaaa)`3`color(white) (aaaa)`27`color(white)(aaaa)`18
`color(white)(aaaaaaaaaaa)` `---------`
`color(white)(aaaaaaaaaaaa)`1`color(white)(aaaa)`9`color(white) (aaaa)`6`color(white)(aaaaaa)`0=remainder
`color(white)(aaaaaaaaaaa)` `---------`

`r-3=0`

`r=3`

`:.`= `r^2+9r+6`