# How do you divide (5x^3-6x^2+3x+11)div(x-2) using synthetic division?

Mar 19, 2017

The remainder is $= 33$ and the quotient is $= 5 {x}^{2} + 4 x + 11$

#### 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 a}$$|$$\textcolor{w h i t e}{a a a a}$$5$$\textcolor{w h i t e}{a a a a}$$- 6$$\textcolor{w h i t e}{a a a a}$$3$$\textcolor{w h i t e}{a a a a}$$11$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$________

$\textcolor{w h i t e}{a a a a}$color(white)(aaaaaaa)|$\textcolor{w h i t e}{a a a a}$color(white)(aaaaa)10$\textcolor{w h i t e}{a a a a}$$8$$\textcolor{w h i t e}{a a a a}$$22$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$________
$\textcolor{w h i t e}{a a a a}$color(white)(aaaaaaa)|$\textcolor{w h i t e}{a a a a}$$5$$\textcolor{w h i t e}{a a a a}$$4$$\textcolor{w h i t e}{a a a a a}$$11$$\textcolor{w h i t e}{a a a a}$$\textcolor{red}{33}$

The remainder is $= 33$ and the quotient is $= 5 {x}^{2} + 4 x + 11$