Question

How do you divide `(y^4-8y^3+10y^2+2y+4)div(y-2)` using synthetic division?

Answer 1

The remainder is `color(red)(0)` and the quotient is `=y^3-6y^2-2y-2`

Explanation:

Let's perform the [synthetic division]

`color(white)(aaaa)` `2` `color(white)(aaaaaa)` `|` `color(white)(aa)` `1` `color(white)(aaaa)` `-8` `color(white)(aaaaaa)` `10` `color(white)(aaaaaaa)` `2` `color(white)(aaaaaaa)` `4`
`color(white)(aaaaaaaaaaaa)`_________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `color(white)(aaaaa)` `2` `color(white)(aaaa)` `-12` `color(white)(aaaaa)` `-4` `color(white)(aaaaaa)` `-4`
`color(white)(aaaaaaaaaaaa)`________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaa)` `1` `color(white)(aaa)` `-6` `color(white)(aaaaa)` `-2` `color(white)(aaaaaa)` `-2` `color(white)(aaaaaaa)` `color(red)(0)`

The remainder is `color(red)(0)` and the quotient is `=y^3-6y^2-2y-2`

`(y^4-8y^3+10y^2+2y+4)/(y-2)=y^3-6y^2-2y-2`