# How do you divide (v^3-10v^2+15v+20)div(v-3) using synthetic division?

##### 1 Answer
Jun 11, 2017

The remainder is $= 2$ and the quotient is $= {v}^{2} - 7 v - 6$

#### Explanation:

Let's perform the synthetic division

$\textcolor{w h i t e}{a a a a}$$3$$\textcolor{w h i t e}{a 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 a a}$$- 10$$\textcolor{w h i t e}{a a a a a a}$$15$$\textcolor{w h i t e}{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 a}$$3$$\textcolor{w h i t e}{a a a a a}$$- 21$$\textcolor{w h i t e}{a a a a}$$- 18$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$________

$\textcolor{w h i t e}{a a a a}$$\textcolor{w h i t e}{a a a a a a a}$$|$$\textcolor{w h i t e}{a a a a}$$1$$\textcolor{w h i t e}{a a a a a a}$$- 7$$\textcolor{w h i t e}{a a a a a}$$- 6$$\textcolor{w h i t e}{a a a a a a}$$\textcolor{red}{2}$

The remainder is $= 2$ and the quotient is $= {v}^{2} - 7 v - 6$

$\frac{{v}^{3} - 10 {v}^{2} + 15 v + 20}{v - 3} = {v}^{2} - 7 v - 6 + \frac{2}{v - 3}$