# How do you divide (x ^ { 2} - 9x + 25) \div ( x - 5)?

Sep 13, 2017

$x - 4 + \frac{5}{x - 5}$

#### Explanation:

$\text{one way is to use the divisor as a factor in the numerator}$

$\text{consider the numerator}$

$\textcolor{red}{x} \left(x - 5\right) \textcolor{m a \ge n t a}{+ 5 x} - 9 x + 25$

$= \textcolor{red}{x} \left(x - 5\right) \textcolor{red}{- 4} \left(x - 5\right) \textcolor{m a \ge n t a}{- 20} + 25$

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

$\text{quotient "=color(red)(x-4)," remainder } = 5$

$\Rightarrow \frac{{x}^{2} - 9 x + 25}{x - 5} = x - 4 + \frac{5}{x - 5}$