Question

How do you divide `(3x^2+4x-x^4-2x^3-4)div(x+2)` using synthetic division?

Answer 1

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

Explanation:

We perform a synthetic division

`color(white)(aaaa)` `-2` `color(white)(aaaa)` `|` `color(white)(aaaa)` `-1` `color(white)(aaaa)` `-2` `color(white)(aaaaa)` `3` `color(white)(aaaaaa)` `4` `color(white)(aaaaaa)` `-4`

`color(white)(aaaaaa)` `color(white)(aaaaa)` `|` `color(white)(aaa)` `color(white)(aaaaaaaaa)` `2` `color(white)(aaaaa)` `0` `color(white)(aaaaa)` `-6` `color(white)(aaaaaa)` `4`

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

`color(white)(aaaa)` `color(white)(aaaaaa)` `color(white)(aaaaaa)` `-1` `color(white)(aaaaaa)` `0` `color(white)(aaaaa)` `3` `color(white)(aaaaa)` `-2` `color(white)(aaaaaa)` `color(red)(0)`

The remainder is `=0`

The quotient is `=-x^3+3x-2`