Question

How do you divide `(x^4-x^3+ 3 x^2-4x-2)/(x+2)`?

Answer 1

The remainder is `42` and the quotient is `=x^3-3x^2+9x-22`

Explanation:

Let's perform the synthetic division

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

`color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `color(white)(aaaaa)` `-2` `color(white)(aaaaaa)` `6` `color(white)(aaaaa)` `-18` `color(white)(aaaa)` `44`

`color(white)(aaaaaaaaa)` #`_________________________________________________________`#

`color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `1` `color(white)(aaaa)` `-3` `color(white)(aaaaaa)` `9` `color(white)(aaaaa)` `-22` `color(white)(aaaa)` `color(red)(42)`

The remainder is `42` and the quotient is `=x^3-3x^2+9x-22`

`(x^4-x^3+3x^2-4x-2)/(x+2)=x^3-3x^2+9x-22+42/(x+2)`