Factoring return

3 x 4 = 12; 3 and 4 are factors of 12. 6 and 2 are factors of 12 as are 1 and 12. If you are asked to factor 12 you write 12 = 3 x 4 or 12 = 2 x 6 or 12 = 1 x 12

In other words you are being asked: What did you multiply together to obtain 12?

In algebra:

3(r + 2) = 3r + 6 3 and (r + 2) are factors of 3r + 6

When you are asked to factor 3r + 6 you are being asked to convert 3r + 6 to 3(r + 2).

In other words you are being asked: What did you multiply together to obtain 3r + 6?

Factor this problem; 4p + 8 =

4p + 8 = 4p + 4(2) 4 and p are factors of each other and
4 and 2 are factors of each other. The largest common factor of 4p and
4(2) is 4. Therefore 4p + 8 = 4(p + 2) Are there other common
factors of 4p + 8? Yes. 4p + 8 = 2(2p + 4) However;
**When asked to factor we want the largest common factor which in this
case is 4. **

Factor 4t + 7t^{2} = 2(2)t + 7t(t) =
t(4 + 7t) t is the only common factor of 4t and 7t^{2}.

Sometimes we cannot factor because there are no common factors.

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

Factor r^{2} + 6r + 9 = (
)( )

r^{2} + 6r + 9 = (r + 3)(r + 3) The
first terms 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 did I know that r^{2} + 6r + 9 would equal (r +
3)(r + 3)? 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 I must multiply (r +
3)(r + 3) and see if the answer equals r^{2} + 6r + 9. If it does, the
answer is correct.

Factor these examples: 1. r^{2}
- r - 20 = answer

2. 6t^{2} - 8t - 8 =
answer