Question

How do you divide `(v^3-10v^2+15v+20)div(v-3)` using synthetic division?

Answer 1

The remainder is `=2` and the quotient is `=v^2-7v-6`

Explanation:

Let's perform the synthetic division

`color(white)(aaaa)` `3` `color(white)(aaaaa)` `|` `color(white)(aaaa)` `1` `color(white)(aaaaaa)` `-10` `color(white)(aaaaaa)` `15` `color(white)(aaaaa)` `20`
`color(white)(aaaaaaaaaaaa)`_________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `color(white)(aaaaaaaa)` `3` `color(white)(aaaaa)` `-21` `color(white)(aaaa)` `-18`
`color(white)(aaaaaaaaaaaa)`________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `1` `color(white)(aaaaaa)` `-7` `color(white)(aaaaa)` `-6` `color(white)(aaaaaa)` `color(red)(2)`

The remainder is `=2` and the quotient is `=v^2-7v-6`

`(v^3-10v^2+15v+20)/(v-3)=v^2-7v-6+2/(v-3)`