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

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Answer 1 · 2018-07-21T23:05:00

#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 #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

#(a+5)(a+6)#

We now have the following:

#((a+5)(a+6))/(a+6)#

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

#((a+5)cancel(a+6))/cancel(a+6)#

We're left with

#a+5#

Hope this helps!