Help for algebra

Help for multiplying:

You know how to multiply two binomials:
(x + 3)(x + 4) = x² + 7x + 12

Today in class, I tried to show that the two numbers in the parenthesis (with the x's) will add together to make the middle term (3 + 4 = 7) and they multiply togther to make the last term (3 * 4 = 12). Using this, we could work backwards.

x² + 9x + 18 = ( _______ )( _______ ).

You know there has to be x's in the beginning of the parenthesis:

x² + 9x + 18 = (x ____ )(x ____ ).

The two numbers that go with the x's will add up to make 9, and multiply to make 18 (the two last terms from the problem). Think, what numbers multiply to make 18, but add up to 9. First, find all the combination's that multiply to make 18.

1x18
2x9
3x6

Which combination when you add makes 9? The last one. 3x6 = 18, and 3+6 = 9, so the two missing numbers are 3 and 6.

x² + 9x + 18 = (x + 3)(x + 6)