How do you find the quotient of $(a^{2} + 11 a + 30) \div (a + 5)$ $(a^2 + 11a + 30) div (a + 5)$ ?

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Answer 1 · 2018-07-21T23:05:00

$a + 5$ $a+5$

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 $11$ $11$ and have a product of $30$ $30$ ?

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

$(a + 5) (a + 6)$ $(a+5)(a+6)$

We now have the following:

$\frac{(a + 5) (a + 6)}{a + 6}$ $((a+5)(a+6))/(a+6)$

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!

How do you find the quotient of (a^2 + 11a + 30) div (a + 5)(a2+11a+30)÷(a+5)(a^2 + 11a + 30) div (a + 5)?