Question

How do you divide `(10r^3-22r^2-17r-21)div(r-3)` using synthetic division?

Answer 1

The answer is `=10r^2+8r+7`

Explanation:

Let's do the division
`10r^3-22r^2-17r-21` `color(white)(aaaa)` `∣` `r-3`
`10r^3-30r^2` `color(white)(aaaaaaaaaaaaaa)` `∣` `10r^2+8r+7`
`color(white)(aa)` `0+8r^2-17r`
`color(white)(aaaa)` `+8r^2-24r`
`color(white)(aaaaaaa)` `0+7r-21`
`color(white)(aaaaaaaaaaa)` `7r-21`
`color(white)(aaaaaaaaaaaa)` `0-0`

So we have `(10r^3-22r^2-17r-21)/(r-3)=10r^2+8r+7`