# How do you divide (3x^2-10x)div(x-6) using synthetic division?

Oct 30, 2016

The answer is $= 3 x + 8 + \frac{48}{x - 6}$

#### Explanation:

Let's do the long division

$3 {x}^{2} - 10 x$$\textcolor{w h i t e}{a a a a}$∣$x - 6$
$3 {x}^{2} - 18 x$$\textcolor{w h i t e}{a a a a}$∣$3 x + 8$
$\textcolor{w h i t e}{a a}$$0 + 8 x$
$\textcolor{w h i t e}{a a a a a}$$8 x - 48$
$\textcolor{w h i t e}{a a a a a a}$$0 + 48$

So let's put it all together
$\frac{3 {x}^{2} - 10 x}{x - 6} = 3 x + 8 + \frac{48}{x - 6}$