# How do you divide (2x^3-11x^2+9x-20)div(x-5) using synthetic division?

Aug 13, 2017

The remainder is $\textcolor{red}{0}$ and the quotient is $= 2 {x}^{2} - x + 4$

#### Explanation:

Let's perform the synthetic division

$\textcolor{w h i t e}{a a a a}$$5$$\textcolor{w h i t e}{a a a a a a}$$|$$\textcolor{w h i t e}{a a}$$2$$\textcolor{w h i t e}{a a a a a a a}$$- 11$$\textcolor{w h i t e}{a a a a a a}$$9$$\textcolor{w h i t e}{a a a a a a a}$$- 20$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$$- - - - - - - - - - - -$

$\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 a a}$$10$$\textcolor{w h i t e}{a a a a a a}$$- 5$$\textcolor{w h i t e}{a a a a a a a a}$$20$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$$- - - - - - - - - - - -$

$\textcolor{w h i t e}{a a a a}$$\textcolor{w h i t e}{a a a a a a a}$$|$$\textcolor{w h i t e}{a a a}$$2$$\textcolor{w h i t e}{a a a a a a}$$- 1$$\textcolor{w h i t e}{a a a a a a a a}$$4$$\textcolor{w h i t e}{a a a a a a a a}$$\textcolor{red}{0}$

The remainder is $\textcolor{red}{0}$ and the quotient is $= 2 {x}^{2} - x + 4$

$\frac{2 {x}^{3} - 11 {x}^{2} + 9 x - 20}{x - 5} = 2 {x}^{2} - x + 4$