How do you find the quotient of #(a^2 + 11a + 30) div (a + 5)#?
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
After some trial and error, we arrive at
We now have the following:
This works out very nicely, as we can now cancel out common factors:
We're left with
Hope this helps!