# How do you find the quotient of (a^2 + 11a + 30) div (a + 5)?

Jul 21, 2018

$a + 5$

#### Explanation:

The key realization is that we should see if we can factor the numerator before we go through the trouble of long division.

To factor the numerator, let's do a little thought experiment:

What two numbers sum up to $11$ and have a product of $30$?

After some trial and error, we arrive at $5$ and $6$. This means we can factor this as

$\left(a + 5\right) \left(a + 6\right)$

We now have the following:

$\frac{\left(a + 5\right) \left(a + 6\right)}{a + 6}$

This works out very nicely, as we can now cancel out common factors:

$\frac{\left(a + 5\right) \cancel{a + 6}}{\cancel{a + 6}}$

We're left with

$a + 5$

Hope this helps!