# How do you divide (x^4+2x^3+ 5 x^2+6x-32)/(x-4) ?

Jun 5, 2017

The remainder is $= 456$ and the quotient is $= {x}^{3} + 6 {x}^{2} + 29 x + 122$

#### 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 a}$$|$$\textcolor{w h i t e}{a a a a}$$1$$\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}$$5$$\textcolor{w h i t e}{a a a a a}$$6$$\textcolor{w h i t e}{a a a a a a a}$$- 32$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$_________

$\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}$$4$$\textcolor{w h i t e}{a a a a a a}$$24$$\textcolor{w h i t e}{a a a a}$$116$$\textcolor{w h i t e}{a a a a a a}$$488$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$________

$\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$$\textcolor{w h i t e}{a a a a a}$$6$$\textcolor{w h i t e}{a a a a a a}$$29$$\textcolor{w h i t e}{a a a a}$$122$$\textcolor{w h i t e}{a a a a a a}$$\textcolor{red}{456}$

$\frac{{x}^{4} + 2 {x}^{3} + 5 {x}^{2} + 6 x - 32}{x - 4} = \left({x}^{3} + 6 {x}^{2} + 29 x + 122\right) + \frac{456}{x - 4}$

The remainder is $= 456$ and the quotient is $= {x}^{3} + 6 {x}^{2} + 29 x + 122$