Question

How do you find the quotient of `(2-x+x^2-x^3-x^4)div(x+2)` using synthetic division?

Answer 1

The remainder is `0` and the quotient is `=-x^3+x^2-x+1`

Explanation:

Let's perform the synthetic division

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

`color(white)(aaaaaaa)` ###|#`color(white)(aaaa)` ###color(white)(aaaaaaaa)#`2` `color(white)(aaaaa)` `-2` `color(white)(aaaaa)` `2` `color(white)(aaaa)` `-2`

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

`color(white)(aaaaaaa)` ###|#`color(white)(aaaa)` `-1` `color(white)(aaaaaa)` `1` `color(white)(aaaa)` `-1` `color(white)(aaaaa)` `1` `color(white)(aaaaaa)` `color(red)(0)`

The remainder is `0` and the quotient is `=-x^3+x^2-x+1`