TRY IT:

Factory^2 + 10y - 11

Here's a harder one:

Factor   a^2 + 7a + 10

We start with

( a     ) ( a     )

Our last term is 10... so, our choices are

1 * 10 and 2 * 5

Which is it? Our middle guy will guide us...

We need a 7.

Can we use a 1 and a 10 to make a 7? No!

So it's the 2 and the 5:

( a   2 ) ( a   5 )

What about the signs?

+2 + 5 = +7

So,    a^2 + 7a + 10 = ( a + 2 ) ( a + 5 )