Question

How do you divide `(x^3+x^2-17x+15)div(x+5)` using synthetic division?

Answer 1

The remainder is `0` and the quotient is `=x^2-4x+3`

Explanation:

Let's perform the synthetic division

`color(white)(aaaa)` `-5` `color(white)(aaaa)` `|` `color(white)(aaaa)` `1` `color(white)(aaaa)` `1` `color(white)(aaaaaa)` `-17` `color(white)(aaaaaaa)` `15`
`color(white)(aaaaaaaaaaaa)`_________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `color(white)(aaa)` `-5` `color(white)(aaaaaaa)` `20` `color(white)(aaaaaa)` `-15`
`color(white)(aaaaaaaaaaaa)`________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaa)` `1` `color(white)(aaa)` `-4` `color(white)(aaaaaaaa)` `3` `color(white)(aaaaaaaa)` `color(red)(0)`

The remainder is `color(red)(0)` and the quotient is `=x^2-4x+3`

`(x^3+x^2-17x+15)/(x+5)=x^2-4x+3`