Question

How do you divide `(10x^4+5x^3+4x^2-9)div(x+1)` using synthetic division?

Answer 1

The quotient is `=10x^3-5x^2+9x-9` and the remainder `=0`

Explanation:

We perform a synthetic division

`color(white)(aaaa)` `-1` `color(white)(aaaa)` `|` `color(white)(aaaa)` `10` `color(white)(aaaa)` `5` `color(white)(aaaaa)` `4` `color(white)(aaaaaa)` `0` `color(white)(aaaa)` `-9`

`color(white)(aaaaaa)` `color(white)(aaaaa)` `|` `color(white)(aaa)` `color(white)(aaaa)` `-10` `color(white)(aaaaa)` `5` `color(white)(aaaaa)` `-9` `color(white)(aaaaa)` `9`

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

`color(white)(aaaa)` `color(white)(aaaaaa)` `color(white)(aaaaaa)` `10` `color(white)(aaa)` `-5` `color(white)(aaaaa)` `9` `color(white)(aaaaa)` `-9` `color(white)(aaaaa)` `color(red)(0)`

The remainder is `=0`

The quotient is `=10x^3-5x^2+9x-9`