# Thread: Factor by grouping

1. ## Factor by grouping

http://i24.tinypic.com/2hncsgh.jpg

I don't understand how to do this...

2. Originally Posted by fluffy_penguin
http://i24.tinypic.com/2hncsgh.jpg

I don't understand how to do this...
Write $3a^2 + 2a - 21 = 3a^2 + (9a - 7a) - 21$

$= (3a^2 + 9a) - (7a + 21)$

$= 3a(a + 3) - 7(a + 3)$

$= (3a - 7)(a + 3)$

-Dan

3. ## Confused

Originally Posted by topsquark
Write $3a^2 + 2a - 21 = 3a^2 + (9a - 7a) - 21$

$= (3a^2 + 9a) - (7a + 21)$

$= 3a(a + 3) - 7(a + 3)$

$= (3a - 7)(a + 3)$

-Dan
How does

$3a^2 + 2a - 21 = 3a^2 + (9a - 7a) - 21$

I have no clue where the $(9a - 7a)$ came from...

4. Originally Posted by fluffy_penguin
How does

$3a^2 + 2a - 21 = 3a^2 + (9a - 7a) - 21$

I have no clue where the $(9a - 7a)$ came from...
we use \bold{ } to make something bold with LaTex

topsquark noticed that 9a - 7a = 2a. how did he do that? well, he could have done it by experience, but there is a method you can do.

take the coefficient of a^2, that is 3 and multiply it by the constant term, that is, -21. the result is -63. now you want two numbers that when multiplied give -63 but when added give 2 (which is the coefficient of the middle term). 9 and -7 are such numbers. now we split the middle term into those two numbers and continue as topsquark did

5. Okay thank you both of you. ^ ^

6. Originally Posted by fluffy_penguin
Okay thank you both of you. ^ ^
you're welcome, come again