# How do you divide (3x^3+4x^2+2x+5)/(x-4) ?

Jul 10, 2018

The remainder is $269$ and the quotient is $= 3 {x}^{2} + 16 x + 66$

#### Explanation:

Let's perform the synthetic division

$\textcolor{w h i t e}{a a a a}$$4$$|$$\textcolor{w h i t e}{a a a a}$$3$$\textcolor{w h i t e}{a a a a}$$4$$\textcolor{w h i t e}{a a a a a a}$$2$$\textcolor{w h i t e}{a a a a a a a}$$5$

$\textcolor{w h i t e}{a a a a a}$$|$$\textcolor{w h i t e}{a a a a}$$\textcolor{w h i t e}{a a a a a}$$12$$\textcolor{w h i t e}{a a a a a}$$64$$\textcolor{w h i t e}{a a a a a}$$264$

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

$\textcolor{w h i t e}{a a a a a}$$|$$\textcolor{w h i t e}{a a a a}$$3$$\textcolor{w h i t e}{a a a a}$$16$$\textcolor{w h i t e}{a a a a a}$$66$$\textcolor{w h i t e}{a a a a a a}$$\textcolor{red}{269}$

The remainder is $269$ and the quotient is $= 3 {x}^{2} + 16 x + 66$

$\frac{3 {x}^{3} + 4 {x}^{2} + 2 x + 5}{x - 4} = \left(3 {x}^{2} + 16 x + 66\right) + \frac{269}{x - 4}$