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}.

Try these problems:

- 5b - 25 = answer
- 6t
^{3}+ 18t = answer - 4p
^{5}+ 12p^{4}- 16p^{2}= answer - 4p
^{5}t^{3}b + 12p^{4}t^{2}b^{2}- 16p^{2}tb^{3}= answer