# How do you divide (m^3+6m^2+9m-5)div(m+1) using synthetic division?

Mar 17, 2017

The remainder is $= - 9$ and the quotient is $= {m}^{2} + 5 m + 4$

#### Explanation:

Let's perform the synthetic division

$\textcolor{w h i t e}{a a a a}$$- 1$$\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}$$6$$\textcolor{w h i t e}{a a a a}$$9$$\textcolor{w h i t e}{a a a a}$$- 5$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$________

$\textcolor{w h i t e}{a a a a}$color(white)(aaaaaaa)|$\textcolor{w h i t e}{a a a a}$color(white)(aaa)-1$\textcolor{w h i t e}{a a}$$- 5$$\textcolor{w h i t e}{a a a a}$$- 4$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$________
$\textcolor{w h i t e}{a a a a}$color(white)(aaaaaaa)|$\textcolor{w h i t e}{a a a a}$$1$$\textcolor{w h i t e}{a a a a}$$5$$\textcolor{w h i t e}{a a a a}$$4$$\textcolor{w h i t e}{a a a a}$$\textcolor{red}{- 9}$

The remainder is $= - 9$ and the quotient is $= {m}^{2} + 5 m + 4$