Question

How do you divide `(9x^3-19x^2-28x+12)div(x-3)` using synthetic division?

Answer 1

The remainder is `=0` and the quotient is `=9x^2+8x-4`

Explanation:

Let's perform the synthetic division

`color(white)(aaaa)` `3` `color(white)(aaaaa)` `|` `color(white)(aaaa)` `9` `color(white)(aaaaaa)` `-19` `color(white)(aaaaaa)` `-28` `color(white)(aaaa)` `12`
`color(white)(aaaaaaaaaaaa)`_________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `color(white)(aaaaaaaa)` `27` `color(white)(aaaaaaa)` `24` `color(white)(aaa)` `-12`
`color(white)(aaaaaaaaaaaa)`________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `9` `color(white)(aaaaaaaa)` `8` `color(white)(aaaaaa)` `-4` `color(white)(aaaaaa)` `color(red)(0)`

`(9x^3-19x^2-28x+12)/(x-3)=(9x^2+8x-4)`

The remainder is `=0` and the quotient is `=9x^2+8x-4`