hey, im trying to do this problem, i figured out the answer but i have to show work. its really easy im just being stupid right now lol so the problem is to factor
4x^2 + 12x + 9
and the answer is 2x = 3 2x + 3 and the original factors are x + 6 but i dont get how i got that into 2x+3

Question

hey, im trying to do this problem, i figured out the answer but i have to show work. its really easy im just being stupid right now lol so the problem is to factor
4x^2  + 12x + 9
and the answer is 2x = 3 2x + 3 and the original factors are x + 6 but i dont get how i got that into 2x+3

anonymous · Answer

ok thank you so much

anonymous · Answer

huh? @bunny5241

anonymous · Answer

oh for the answer to the question

anonymous · Answer

@bunny5241  lol did you have the same question?

anonymous · Answer

yeah for some homework i had

anonymous · Answer

@bunny5241 can you help me show work

anonymous · Answer

how do you get the 2x + 3 part? do you divide x+6 by 2 or 4?

anonymous · Answer

ah! i will have to reply in a while i have to leave right now bye.

anonymous · Answer

where did you get the (x + 6) from?

You can factor 4x^2 + 12x + 9 as (2x + 3)(2x + 3)
but I didn't understand why you were talking about (x + 6).

anonymous · Answer

i have to show work, 2x+3 is the answer. but when your factoring that i multiplied 4 x 9 to get 36 and then i found the greatest common factor which is 6 so (x+6)(x+6) and then i divided by 4 @JakeV8

anonymous · Answer

I'm not familiar with factoring it that way.

The mental process I would do is like this:

1.  what are factors of 9?  (since that's the last number in the expression...)
It could be 9 and 1, or it could be 3 and 3.

2.  What are the factors of 4?  (the coefficient on x^2 in the expression...)
It could be 4 and 1, or it could be 2 and 2.

3.  Is there some combination of the factors of 9 and the factors of 4, that when you multiply one of each pair of factors and then add, you get 12?
For example:
(4x + 3)(x + 3) = 4x^2 + 3x + 12x + 9 = 4x^2 + 15x + 9 <<-- DOESN'T WORK

So, then I noticed that if I choose the factors of 4 as 2 and 2, and if I choose the factors of 9 to be 3 and 3, then (2x + 3)(2x + 3) does work.

I'm not saying you're method is wrong, but I haven't seen it done the way you described it.

anonymous · Answer

yah, my teacher taught us this way and its rather confusing, but thanks for the help! we both ended up with the same answer :) @JakeV8

anonymous · Answer

Interesting... well, glad you understand how to factor it some way, even if your teacher's method confuses you (and me!!).

Glad to help... good luck :)