# How do you divide x^2/(2x + 4 )?

Apr 17, 2017

See below.

#### Explanation:

We have that

${x}^{2} = q \left(x\right) \left(2 x + 4\right) + r \left(x\right)$

where $q \left(x\right)$ is the quocient, and $r \left(x\right)$ is the remainder

Analyzing the degrees involved we have:

$q \left(x\right) = a x + b$

$r \left(x\right) = c$

so

${x}^{2} = 2 a {x}^{2} + 2 \left(b + 2 a\right) x + 4 b + c$

so we need

$\left\{\begin{matrix}2 a = 1 \\ b + 2 a = 0 \\ 4 b + c = 0\end{matrix}\right.$

Solving for $a , b , c$ we have $a = \frac{1}{2} , b = - 1 , c = 4$

and finally

$q \left(x\right) = \frac{x}{2} - 1$

$r \left(x\right) = 4$