# How do you find the quotient of (2-x+x^2-x^3-x^4)div(x+2) using synthetic division?

Jun 29, 2018

The remainder is $0$ and the quotient is $= - {x}^{3} + {x}^{2} - x + 1$

#### Explanation:

Let's perform the synthetic division

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

$\textcolor{w h i t e}{a a a a a a a}$|color(white)(aaaa)color(white)(aaaaaaaa)2$\textcolor{w h i t e}{a a a a a}$$- 2$$\textcolor{w h i t e}{a a a a a}$$2$$\textcolor{w h i t e}{a a a a}$$- 2$

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

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

The remainder is $0$ and the quotient is $= - {x}^{3} + {x}^{2} - x + 1$