# How do you use synthetic division to divide (5x^3-6x^2+8)div(x-4)?

May 14, 2017

The remainder is $= 232$ and the quotient is $= 5 {x}^{2} + 14 x + 56$

#### Explanation:

Let's perform the synthetic division

Let $f \left(x\right) = 5 {x}^{3} - 6 {x}^{2} + 8$

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}$$5$$\textcolor{w h i t e}{a a a a a a}$$- 6$$\textcolor{w h i t e}{a a a a a a}$$0$$\textcolor{w h i t e}{a a a a a a a}$$8$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$_________

$\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}$$20$$\textcolor{w h i t e}{a a a a a a}$$56$$\textcolor{w h i t e}{a a a a a}$$224$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$________

$\textcolor{w h i t e}{a a a a}$$\textcolor{w h i t e}{a a a a a a a}$$|$$\textcolor{w h i t e}{a a a a}$$5$$\textcolor{w h i t e}{a a a a a}$$14$$\textcolor{w h i t e}{a a a a a a a}$$56$$\textcolor{w h i t e}{a a a a a}$$\textcolor{red}{232}$

$f \left(x\right) = \left(5 {x}^{2} + 14 x + 56\right) + \frac{232}{x - 4}$

The remainder is $= 232$