# How do you divide (4x^3 + 2x -15) / (2 x^2-1 )  using polynomial long division?

##### 1 Answer
Nov 21, 2017

The quotient is $2 x$ and the remainder is $= 4 x - 15$

#### Explanation:

Perform the long division

$\textcolor{w h i t e}{a a a a}$$4 {x}^{3} + 0 {x}^{2} + 2 x - 15$$\textcolor{w h i t e}{a a a a}$$|$$2 {x}^{2} - 1$

$\textcolor{w h i t e}{a a a a}$$4 {x}^{3} + 0 {x}^{2} - 2 x$$\textcolor{w h i t e}{a a a a a a a a a}$$|$$2 x$

$\textcolor{w h i t e}{a a a a}$$0 {x}^{3} + 0 {x}^{2} + 4 x - 15$

The quotient is $2 x$ and the remainder is $= 4 x - 15$

So,

$\frac{4 {x}^{3} + 0 {x}^{2} + 2 x - 15}{2 {x}^{2} - 1} = 2 x + \frac{4 x - 15}{2 {x}^{2} - 1}$