# How do you divide (x^4+5x^3-2x^2-4x+4)div(x+3) using synthetic division?

Sep 1, 2017

The remainder is $\textcolor{red}{- 56}$ and the quotient is $= {x}^{3} + 2 {x}^{2} - 8 x + 20$

#### 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}$$5$$\textcolor{w h i t e}{a a a a a a}$$- 2$$\textcolor{w h i t e}{a a a a}$$- 4$$\textcolor{w h i t e}{a a 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}$$\textcolor{w h i t e}{a a a a a a a}$$|$$\textcolor{w h i t e}{a a a a}$$\textcolor{w h i t e}{a a a a a}$$- 3$$\textcolor{w h i t e}{a a a a a a}$$- 6$$\textcolor{w h i t e}{a a a a a}$$24$$\textcolor{w h i t e}{a a a a}$$- 60$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$$- - - - - - - - - - - -$

$\textcolor{w h i t e}{a a a a}$$\textcolor{w h i t e}{a a a a a a a}$$|$$\textcolor{w h i t e}{a a}$$1$$\textcolor{w h i t e}{a a a a a a a a}$$2$$\textcolor{w h i t e}{a a a a a a}$$- 8$$\textcolor{w h i t e}{a a a a a}$$20$$\textcolor{w h i t e}{a a a}$$\textcolor{red}{- 56}$

The remainder is $\textcolor{red}{- 56}$ and the quotient is $= {x}^{3} + 2 {x}^{2} - 8 x + 20$

$\frac{{x}^{4} + 5 {x}^{3} - 2 {x}^{2} - 4 x + 4}{x + 3} = {x}^{3} + 2 {x}^{2} - 8 x + 20 - \frac{56}{x + 3}$