# How do you divide (x^3+6x^2-4x+3)div(x+2)?

Feb 21, 2017

The remainder is $= 27$ and the quotient is ${x}^{2} + 4 x - 12$

#### Explanation:

We 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}$$|$$\textcolor{w h i t e}{a a a a}$$1$$\textcolor{w h i t e}{a a a a}$$6$$\textcolor{w h i t e}{a a a a a}$$- 4$$\textcolor{w h i t e}{a a a}$$3$

$\textcolor{w h i t e}{a a a a a a}$$\textcolor{w h i t e}{a a a a a}$$|$$\textcolor{w h i t e}{a a a a a}$$\textcolor{w h i t e}{a a}$$- 2$$\textcolor{w h i t e}{a a a a}$$- 8$$\textcolor{w h i t e}{a a a a}$$24$

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

$\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}$$4$$\textcolor{w h i t e}{a a a a}$$- 12$$\textcolor{w h i t e}{a a a a}$$\textcolor{red}{27}$

The remainder is $= 27$

The quotient is $= {x}^{2} + 4 x - 12$