# How do you divide (r^3+6r^2-21r-18) div (r-3) using synthetic division?

Jan 20, 2017

$= {r}^{2} + 9 r + 6$

#### Explanation:

$\left({r}^{3} + 6 {r}^{2} - 21 r - 18\right) \div \left(r - 3\right)$

$\textcolor{w h i t e}{a a a a}$$3 |$
$\textcolor{w h i t e}{a a a a a a a a a a a}$$- - - - - - - - -$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$1$\textcolor{w h i t e}{a a a a}$6color(white) (aaaa)-21$\textcolor{w h i t e}{a a a a}$-18
$\textcolor{w h i t e}{a a a a a a a a a a a a}$$\textcolor{w h i t e}{a a a a a}$3color(white) (aaaa)27$\textcolor{w h i t e}{a a a a}$18
$\textcolor{w h i t e}{a a a a a a a a a a a}$$- - - - - - - - -$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$1$\textcolor{w h i t e}{a a a a}$9color(white) (aaaa)6$\textcolor{w h i t e}{a a a a a a}$0=remainder
$\textcolor{w h i t e}{a a a a a a a a a a a}$$- - - - - - - - -$

$r - 3 = 0$

$r = 3$

$\therefore$= ${r}^{2} + 9 r + 6$