# How do you divide (m^3-13m^2+24m+18)div(m-3) using synthetic division?

Feb 28, 2017

The remainder is $= 0$
The quotient is $= {m}^{2} - 10 m - 6$

#### Explanation:

We perform a synthetic division

$\textcolor{w h i t e}{a a a a}$$3$$\textcolor{w h i t e}{a a a a}$$|$$\textcolor{w h i t e}{a a a a}$$1$$\textcolor{w h i t e}{a a a a}$$- 13$$\textcolor{w h i t e}{a a a a a a a}$$24$$\textcolor{w h i t e}{a a a a a a}$$18$$\textcolor{w h i t e}{a a a a a a}$

$\textcolor{w h i t e}{a a a a a a}$$\textcolor{w h i t e}{a a a}$$|$$\textcolor{w h i t e}{a a a}$$\textcolor{w h i t e}{a a a a a a a a a}$$3$$\textcolor{w h i t e}{a a a a a}$$- 30$$\textcolor{w h i t e}{a a a a}$$- 18$$\textcolor{w h i t e}{a a a a a a}$

$\textcolor{w h i t e}{a a a a a a a a a a}$------------------------------------------------------------

$\textcolor{w h i t e}{a a a a} \textcolor{w h i t e}{a a a a a a} \textcolor{w h i t e}{a a a a a a} 1 \textcolor{w h i t e}{a a a a} - 10$$\textcolor{w h i t e}{a a a a a} - 6 \textcolor{w h i t e}{a a a a a} \textcolor{w h i t e}{a a} \textcolor{red}{0}$

The remainder is $= 0$

The quotient is $= {m}^{2} - 10 m - 6$