# FACTORING

##

Sometimes we cannot factor because there are no common
factors.

For example 4t + 9 = 2(2)t + 3(3)

Multiply (r + 3)(r + 3) =
answer
Now reverse the procedure and factor r^{2} + 6r + 9 = (
)( )

The
first terms in the parenthesis when multiplied together must equal r^{2}
and the second terms when multiplied together must
equal + 9. How do
we obtain the middle term? Notice that when we add 3
+ 3 together we get 6.

How do I know that p^{2} + 8p + 16 will equal (p +
4)(p + 4)? I used a very important and old mathematical principal.

## I guessed!

##

After you do enough of these problems it becomes an educated
guess. To verify that the answer is correct multiply (p + 4)(p + 4) and see if
the results equals p^{2} + 8p + 16. If it does, the
answer is correct.

Factor these examples:

- r
^{2}
- r - 20 = answer
- 6t
^{2} - 8t - 8 = answer
- 24p
^{2} - 34p + 12 = answer

return