Question

How do you divide `(n^4+5n^3-6n+3)div(n+3)` using synthetic division?

Answer 1

The remainder is `=-33` and the quotient is `=n^3+2n^2-6n+12`

Explanation:

Let's perform the synthetic division

`color(white)(aaaa)` `-3` `color(white)(aaaaa)` `|` `color(white)(aaaa)` `1` `color(white)(aaaaaa)` `5` `color(white)(aaaaaa)` `0` `color(white)(aaaaa)` `-6` `color(white)(aaaaaaa)` `3`
`color(white)(aaaaaaaaaaaa)`_________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `color(white)(aaaaaa)` `-3` `color(white)(aaaaaa)` `-6` `color(white)(aaaa)` `18` `color(white)(aaaaa)` `-36`
`color(white)(aaaaaaaaaaaa)`________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `1` `color(white)(aaaaaaa)` `2` `color(white)(aaaaaa)` `-6` `color(white)(aaaa)` `12` `color(white)(aaaaa)` `color(red)(-33)`

`(n^4+5n^3-6n+3)/(n+3)=(n^3+2n^2-6n+12)-33/(n+3)`

The remainder is `=-33` and the quotient is `=n^3+2n^2-6n+12`