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

May 20, 2017

The quotient is $= \left(x + 2\right)$ and the remainder is $= \left(- 3 x - 6\right)$

#### Explanation:

Let's perform the long division

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

$\textcolor{w h i t e}{a a a a a a a a a a a a a a a}$${x}^{3} + 00 + x$

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

$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a a}$$+ 2 {x}^{2} - 00 + 2$

$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a a a a}$$+ 0 - 3 x - 6$

Therefore,

$\frac{{x}^{3} + 2 {x}^{2} - 2 x - 4}{{x}^{2} + 1} = x + 2 + \frac{- 3 x - 6}{{x}^{2} + 1}$

The quotient is $= \left(x + 2\right)$ and the remainder is $= \left(- 3 x - 6\right)$