# How do you divide (2n^3+62n-26n^2+4)div(2n-6) using synthetic division?

Jun 11, 2017

The remainder is $= 269$ and the quotient is $= {n}^{2} + 34 n + 89$

#### 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}$$31$$\textcolor{w h i t e}{a a a a a a}$$- 13$$\textcolor{w h i t e}{a a a a a}$$2$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$_________

$\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}$$3$$\textcolor{w h i t e}{a a a a a a a}$$102$$\textcolor{w h i t e}{a a a a}$$267$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$________

$\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$$\textcolor{w h i t e}{a a a a a a}$$34$$\textcolor{w h i t e}{a a a a a a a}$$89$$\textcolor{w h i t e}{a a a a}$$\textcolor{red}{269}$

The remainder is $= 269$ and the quotient is $= {n}^{2} + 34 n + 89$

$\frac{{n}^{3} + 31 {n}^{2} - 13 n + 2}{n - 3} = {n}^{2} + 34 n + 89 + \frac{269}{n - 3}$

N.B The numerator and denominator were divided by the common factor $2$