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

Feb 28, 2017

The remainder is $= 0$
The quotient is $= - {x}^{3} + 3 x - 2$

#### Explanation:

We perform a synthetic division

$\textcolor{w h i t e}{a a a a}$$- 2$$\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}$$- 2$$\textcolor{w h i t e}{a a a a a}$$3$$\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}$$- 4$

$\textcolor{w h i t e}{a a a a a a}$$\textcolor{w h i t e}{a a a a a}$$|$$\textcolor{w h i t e}{a a a}$$\textcolor{w h i t e}{a a a a a a a a a}$$2$$\textcolor{w h i t e}{a a a a a}$$0$$\textcolor{w h i t e}{a a a a a}$$- 6$$\textcolor{w h i t e}{a a a a a a}$$4$

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

$\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 a a}$$0$$\textcolor{w h i t e}{a a a a a}$$3$$\textcolor{w h i t e}{a a a a a}$$- 2$$\textcolor{w h i t e}{a a a a a a}$$\textcolor{red}{0}$

The remainder is $= 0$

The quotient is $= - {x}^{3} + 3 x - 2$