Question

How do you divide `(x^3-6x^2-6x+9)div(x+1)` using synthetic division?

Answer 1

The quotient is `=x^2-7x+1`
The remainder is `=8`

Explanation:

let's do the long division

`color(white)(aaaa)` `x^3-6x^2-6x+9` `color(white)(aa)` `∣` `x+1`
`color(white)(aaaa)` `x^3+x^2` `color(white)(aaaaaaaaaaa)` `∣` `x^2-7x+1`
`color(white)(aaaaa)` `0-7x^2-6x`
`color(white)(aaaaaaa)` `-7x^2-7x`
`color(white)(aaaaaaaaaaa)` `0+x+9`
`color(white)(aaaaaaaaaaaaa)` `+x+1`
`color(white)(aaaaaaaaaaaaa)` `+0+8`

So the quotient is `=x^2-7x+1`

and the remainder `=8`