# How do you find the quotient of (x^2-5x-16)div(x+2)?

Feb 10, 2017

$x - 7$

#### Explanation:

Using the following $\textcolor{b l u e}{\text{algebraic manipulation}}$

$\text{Using the divisor "(x+2)" as a factor in the numerator}$

$\frac{{x}^{2} - 5 x - 16}{x + 2}$

$= \frac{\textcolor{red}{x} \left(x + 2\right) + \left(\textcolor{b l u e}{- 2 x} - 5 x\right) - 16}{x + 2}$

$= \frac{\textcolor{red}{x} \left(x + 2\right) \textcolor{red}{- 7} \left(x + 2\right) + \left(\textcolor{b l u e}{+ 14} - 16\right)}{x + 2}$

$= \textcolor{red}{x - 7} - \frac{2}{x + 2}$

$\Rightarrow \text{quotient } = x - 7$

Feb 10, 2017

$x - 7 = q u o t i e n t$ and remainder $= - 2$

#### Explanation:

$\textcolor{w h i t e}{a a a a a a a a a a}$$x - 7$
$\textcolor{w h i t e}{a a a a a a a a a a}$$- - - - - -$
$\textcolor{w h i t e}{a a a a} x + 4$$|$${x}^{2} - 5 x - 16$color(white) (aaaa)∣color(blue)
$\textcolor{w h i t e}{a a a a a a a a a a}$${x}^{2} + 2 x$color(white)
$\textcolor{w h i t e}{a a a a a a a a a a}$$- - - -$
$\textcolor{w h i t e}{a a a a a a a a a a a}$$0 - 7 x - 16$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$- 7 x - 14$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a}$$- - -$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a}$$0 - 2$

remainder is $= - 2$ and the quotient is $= x - 7$