# How do you divide (x^4+9)div(x+3) using synthetic division?

Sep 2, 2017

The remainder is $\textcolor{red}{90}$ and the quotient is $= {x}^{3} - 3 {x}^{2} + 9 x - 27$

#### Explanation:

Let's perform the synthetic division

$\textcolor{w h i t e}{a a}$$- 3$$\textcolor{w h i t e}{a a a a a}$$|$$\textcolor{w h i t e}{a a a}$$1$$\textcolor{w h i t e}{a a a a a a a a}$$0$$\textcolor{w h i t e}{a a a a a a}$$0$$\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}$$9$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$$- - - - - - - - - - - -$

$\textcolor{w h i t e}{a a a a}$$\textcolor{w h i t e}{a a a a a a}$$|$$\textcolor{w h i t e}{a a a a a}$$\textcolor{w h i t e}{a a a a a}$$- 3$$\textcolor{w h i t e}{a a a a a a}$$9$$\textcolor{w h i t e}{a a a a a}$$- 27$$\textcolor{w h i t e}{a a a a a}$$81$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$$- - - - - - - - - - - -$

$\textcolor{w h i t e}{a a a a}$$\textcolor{w h i t e}{a a a a a a}$$|$$\textcolor{w h i t e}{a a a}$$1$$\textcolor{w h i t e}{a a a a a a}$$- 3$$\textcolor{w h i t e}{a a a a a a}$$9$$\textcolor{w h i t e}{a a a a a}$$- 27$$\textcolor{w h i t e}{a a a a a}$$\textcolor{red}{90}$

The remainder is $\textcolor{red}{90}$ and the quotient is $= {x}^{3} - 3 {x}^{2} + 9 x - 27$

$\frac{{x}^{4} + 9}{x + 3} = {x}^{3} - 3 {x}^{2} + 9 x - 27 + \frac{90}{x + 3}$