Question

How do you divide `(2x^3-11x^2+9x-20)div(x-5)` using synthetic division?

Answer 1

The remainder is `color(red)(0)` and the quotient is `=2x^2-x+4`

Explanation:

Let's perform the synthetic division

`color(white)(aaaa)` `5` `color(white)(aaaaaa)` `|` `color(white)(aa)` `2` `color(white)(aaaaaaa)` `-11` `color(white)(aaaaaa)` `9` `color(white)(aaaaaaa)` `-20`
`color(white)(aaaaaaaaaaaa)` `------------`

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `color(white)(aaaaaaa)` `10` `color(white)(aaaaaa)` `-5` `color(white)(aaaaaaaa)` `20`
`color(white)(aaaaaaaaaaaa)` `------------`

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaa)` `2` `color(white)(aaaaaa)` `-1` `color(white)(aaaaaaaa)` `4` `color(white)(aaaaaaaa)` `color(red)(0)`

The remainder is `color(red)(0)` and the quotient is `=2x^2-x+4`

`(2x^3-11x^2+9x-20)/(x-5)=2x^2-x+4`