Question

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

Answer 1

The remainder is `color(red)(-56)` and the quotient is `=x^3+2x^2-8x+20`

Explanation:

Let's perform the synthetic division

`color(white)(aa)` `-3` `color(white)(aaaaa)` `|` `color(white)(aaa)` `1` `color(white)(aaaaaaaa)` `5` `color(white)(aaaaaa)` `-2` `color(white)(aaaa)` `-4` `color(white)(aaaaaa)` `4`
`color(white)(aaaaaaaaaaaa)` `------------`

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `color(white)(aaaaa)` `-3` `color(white)(aaaaaa)` `-6` `color(white)(aaaaa)` `24` `color(white)(aaaa)` `-60`
`color(white)(aaaaaaaaaaaa)` `------------`

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aa)` `1` `color(white)(aaaaaaaa)` `2` `color(white)(aaaaaa)` `-8` `color(white)(aaaaa)` `20` `color(white)(aaa)` `color(red)(-56)`

The remainder is `color(red)(-56)` and the quotient is `=x^3+2x^2-8x+20`

`(x^4+5x^3-2x^2-4x+4)/(x+3)=x^3+2x^2-8x+20-56/(x+3)`