# How do you divide (2x^2+4x-4)div(x-2) using synthetic division?

Oct 27, 2016

The answer is $\frac{2 {x}^{2} + 4 x - 4}{x - 2} = 2 x + 8 + \frac{12}{x - 2}$

#### Explanation:

Let's do the long division
$2 {x}^{2} + 4 x - 4$$\textcolor{w h i t e}{a a a a a}$∣$x - 2$
$2 {x}^{2} - 4 x$$\textcolor{w h i t e}{a a a a a a a a a}$∣$2 x + 8$
$\textcolor{w h i t e}{a a}$$0 + 8 x - 4$
$\textcolor{w h i t e}{a a}$$0 + 8 x - 16$
$\textcolor{w h i t e}{a a a a a a}$$0 + 12$

So $\frac{2 {x}^{2} + 4 x - 4}{x - 2} = 2 x + 8 + \frac{12}{x - 2}$

The remainder can be obtained
let $f \left(x\right) = 2 {x}^{2} + 4 x - 4$
then $f \left(2\right) = 2 \cdot {2}^{2} + 4 \cdot 2 - 4 = 12$