# How do you divide (4x^3+5x^2-2x-5)/(x^2+4)?

Apr 28, 2017

$4 x + 5 - \frac{18 x + 25}{{x}^{2} + 4}$

#### Explanation:

One way is to use the divisor as a factor in the numerator.

$\textcolor{m a \ge n t a}{\text{Add/Subtract}}$ terms that are being added/subtracted as a consequence.

$\text{consider the numerator}$

$\textcolor{red}{4 x} \left({x}^{2} + 4\right) \textcolor{m a \ge n t a}{- 16 x} \textcolor{red}{+ 5} \left({x}^{2} + 4\right) \textcolor{m a \ge n t a}{- 20} - 2 x - 5$

$= \textcolor{red}{4 x} \left({x}^{2} + 4\right) \textcolor{red}{+ 5} \left({x}^{2} + 4\right) - 18 x - 25$

$\text{quotient " =color(red)(4x+5), "remainder } = - \left(18 x + 25\right)$

$\Rightarrow \frac{4 {x}^{3} + 5 {x}^{2} - 2 x - 5}{{x}^{2} + 4} = 4 x + 5 - \frac{18 x + 25}{{x}^{2} + 4}$