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 + 7t2 = 2(2)t + 7t(t) = t(4 + 7t) t is the only common factor of 4t and 7t2.
Sometimes we cannot factor because there are no common factors.
For example 4t + 9 = 2(2)t + 3(3)
Factor r2 + 6r + 9 = ( )( )
r2 + 6r + 9 = (r + 3)(r + 3) The first terms when multiplied together must equal r2 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 r2 + 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 r2 + 6r + 9. If it does, the answer is correct.
Factor these examples: 1. r2 - r - 20 = answer
2. 6t2 - 8t - 8 = answer