Question

How do you find the quotient of `(2s^3+3s^2-9s-10) div (s-2)` using synthetic division?

Answer 1

The quotient is `=2s^2+7s+5`

Explanation:

Let's perform the synthetic division

`color(white)(aaaa)` `2` `color(white)(aaaaa)` `|` `color(white)(aaaa)` `2` `color(white)(aaaaaa)` `3` `color(white)(aaaaaa)` `-9` `color(white)(aaaa)` `-10`
`color(white)(aaaaaaaaaaaa)`_________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `color(white)(aaaaaa)` `4` `color(white)(aaaaaaa)` `14` `color(white)(aaaaa)` `10`
`color(white)(aaaaaaaaaaaa)`________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `2` `color(white)(aaaaa)` `7` `color(white)(aaaaaaaa)` `5` `color(white)(aaaaaa)` `color(red)(0)`

`(2s^3+3s^2-9s-10)/(s-2)=(2s^2+7s+5)`

The remainder is `=0` and the quotient is `=2s^2+7s+5`