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

Oct 30, 2016

The answer is $= 10 {r}^{2} + 8 r + 7$

#### Explanation:

Let's do the division
$10 {r}^{3} - 22 {r}^{2} - 17 r - 21$$\textcolor{w h i t e}{a a a a}$∣$r - 3$
$10 {r}^{3} - 30 {r}^{2}$$\textcolor{w h i t e}{a a a a a a a a a a a a a a}$∣$10 {r}^{2} + 8 r + 7$
$\textcolor{w h i t e}{a a}$$0 + 8 {r}^{2} - 17 r$
$\textcolor{w h i t e}{a a a a}$$+ 8 {r}^{2} - 24 r$
$\textcolor{w h i t e}{a a a a a a a}$$0 + 7 r - 21$
$\textcolor{w h i t e}{a a a a a a a a a a a}$$7 r - 21$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$$0 - 0$

So we have $\frac{10 {r}^{3} - 22 {r}^{2} - 17 r - 21}{r - 3} = 10 {r}^{2} + 8 r + 7$