# How do you divide (4n^2+7n-5)div(n+3) and identify any restrictions on the variable?

Nov 1, 2017

$4 n - 5 + \frac{10}{n + 3}$

#### Explanation:

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

$\text{consider the numerator}$

$\textcolor{red}{4 n} \left(n + 3\right) \textcolor{m a \ge n t a}{- 12 n} + 7 n - 5$

$= \textcolor{red}{4 n} \left(n + 3\right) \textcolor{red}{- 5} \left(n + 3\right) \textcolor{m a \ge n t a}{+ 15} - 5$

$= \textcolor{red}{4 n} \left(n + 3\right) \textcolor{red}{- 5} \left(n + 3\right) + 10$

$\text{quotient "=color(red)(4n-5)," remainder } = 10$

$\Rightarrow \frac{4 {n}^{2} + 7 n - 5}{n + 3} = 4 n - 5 + \frac{10}{n + 3}$

$\text{with restriction } n \ne - 3$