﻿ Factoring

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

return