# How do you find the quotient of (x^2+x-20)div(x-4)?

Jun 12, 2017

$x + 5$

#### Explanation:

$\textcolor{w h i t e}{w w w w w} x + 5$
x-4 )bar(x^2+x-20)
$\textcolor{w h i t e}{w w w} \underline{\textcolor{red}{-} {x}^{2} \textcolor{red}{+} 4 x} \text{ } \leftarrow$ subtract
$\textcolor{w h i t e}{w w w w w w w w} 5 x - 20$
$\textcolor{w h i t e}{w w n \ldots . . w w} \textcolor{red}{-} \underline{5 x \textcolor{red}{+} 20}$
$\textcolor{w h i t e}{w w w w w w w w w w w w w w} 0 \text{ }$ remainder

$\left({x}^{2} + x - 20\right) \div \left(x - 4\right) = x + 5$

Jun 12, 2017

$x + 5$

#### Explanation:

$\text{factorise the numerator and simplify}$

$\Rightarrow \frac{{x}^{2} + x - 20}{x - 4}$

$= \frac{\left(x + 5\right) \cancel{\left(x - 4\right)}}{\cancel{\left(x - 4\right)}}$

$= x + 5 \leftarrow \textcolor{red}{\text{ quotient}}$

Jun 12, 2017

Factorise and cancel like factors.

$x + 5$

#### Explanation:

In a division such as $48 \div 6$, we could find the quotient by finding factors:

$\frac{48}{6} = \frac{8 \times 6}{6} \text{ } \leftarrow$ like factors can cancel $\text{ } \frac{6}{6} = 1$

$\frac{8 \times \cancel{6}}{\cancel{6}} = 8$

In the same way we can find the quotient by factorising the numerator:

$\frac{{x}^{2} + x - 20}{\left(x - 4\right)} = \frac{\left(x + 5\right) \left(x - 4\right)}{\left(x - 4\right)}$

Cancel the like factors:

$\frac{\left(x + 5\right) \cancel{\left(x - 4\right)}}{\cancel{\left(x - 4\right)}}$

$= x + 5$