# How do you find the quotient of (h^3+2h^2-3h+9)/(h+3) using synthetic division?

Jul 5, 2018

The remainder is $9$ and the quotient is $= {h}^{2} - h$

#### Explanation:

Let's perform the synthetic division

$\textcolor{w h i t e}{a a a a}$$- 3$$|$$\textcolor{w h i t e}{a a a a}$$1$$\textcolor{w h i t e}{a a a a a}$$2$$\textcolor{w h i t e}{a a a a a a}$$- 3$$\textcolor{w h i t e}{a a a a a a a}$$9$

$\textcolor{w h i t e}{a a a a a a a}$|color(white)(aaaa)color(white)(aaaa)-3$\textcolor{w h i t e}{a a a a a a a}$$3$$\textcolor{w h i t e}{a a a a a a a}$$0$

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

$\textcolor{w h i t e}{a a a a a a a}$|color(white)(aaaa)$1$$\textcolor{w h i t e}{a a a}$$- 1$$\textcolor{w h i t e}{a a a a a a a}$$0$$\textcolor{w h i t e}{a a a a a a a}$$\textcolor{red}{9}$

The remainder is $9$ and the quotient is $= {h}^{2} - h$

Therefore,

$\frac{{h}^{3} + 2 {h}^{2} - 3 h + 9}{h + 3} = \left({h}^{2} - h\right) + \frac{9}{h + 3}$