# How do you find the quotient of m^2 – 3m – 28 ÷ m + 4?

Dec 25, 2015

To find the quotient of this particular problem, factorize ${m}^{2} - 3 m - 28$ and divide the result by (m+4). The working and explanation given below.

#### Explanation:

There are many ways in which you can do this problem. If you are comfortable with factoring quadratic trinomials then the following way would be useful.

Our question is ${m}^{2} - 3 m - 28 \div m + 4$

Let us rewrite it as $\frac{{m}^{2} - 3 m - 28}{m + 4}$

Factoring the numerator : ${m}^{2} - 3 m - 28 = \left(m - 7\right) \left(m + 4\right)$

$\frac{\left(m - 7\right) \left(m + 4\right)}{m + 4}$
((m-7)(cancel(m+4)))/(cancel(m+4)  $= m - 7$

The quotient is $m - 7$