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

Apr 5, 2017

$\frac{x - 1}{2}$

#### Explanation:

$\text{ } {x}^{2} + x - 2$
$\textcolor{m a \ge n t a}{\frac{1}{2} x} \left(2 x + 4\right) \to \text{ "ul(x^2+2x) larr" subtract}$
$\text{ } 0 - x - 2$
$\textcolor{m a \ge n t a}{- \frac{1}{2}} \left(2 x + 4\right) \to \text{ "ul( -x-2) larr" subtract}$
$\text{ "0+0 larr" remainder}$

As the remainder is zero the division is exact.

$\frac{{x}^{2} + x - 2}{2 x + 4} = \textcolor{m a \ge n t a}{\frac{x}{2} - \frac{1}{2}} \to \frac{x - 1}{2}$

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$\textcolor{b r o w n}{\text{The above is actually the same process as the traditional method.}}$$\textcolor{b r o w n}{\text{The only difference is the format chosen.}}$