Question

How do you divide using synthetic division: `(2x^3 - 4x^2 - 7x + 5)/(x - 3)`?

Answer 1

The remainder is `=2` and the quotient is `=2x^2+2x-1`

Explanation:

We perform the synthetic division

`color(white)(aaaa)` `3` `color(white)(aaaa)` `|` `color(white)(aaaa)` `2` `color(white)(aaaa)` `-4` `color(white)(aaaaa)` `-7` `color(white)(aaa)` `5`

`color(white)(aaaaaa)` `color(white)(aaa)` `|` `color(white)(aaa)` `color(white)(aaaaaaaa)` `6` `color(white)(aaaaaa)` `6` `color(white)(aaa)` `-3`

`color(white)(aaaaaaaaaa)`------------------------------------------------------------

`color(white)(aaaa)` `color(white)(aaaaaa)` `color(white)(aaaaaa)` `2` `color(white)(aaaa)` `2` `color(white)(aaaaa)` `-1` `color(white)(aaaaa)` `color(red)(2)`

The remainder is `=2`

The quotient is `=2x^2+2x-1`

Verification, by using the remainder theorem

`f(3)=54-36-21+5=59-57=2`