Hi Craig
This one is a little tricky so hopefully this will make sense. First thing is to factor out a 4 which is common to all the terms and put it aside for the moment:
4(4x^2-4x-3)
Now you have to take the middle term the -4x and break it apart into 2 terms that sum to -4x which will then lead to a common factorization of both 4x^2 and -3, and that is the tough part.
You can try breaking it into -1x and -3x or -2x and -2x and neither work, then you try the fancy ones, the one I found that works is 2x and -6x which sums to -4x.
Your equation is 4x^2 + 2x - 6x -3
Now factor the 2 sections:
4x^2 + 2x becomes 2x (2x + 1)
-6x -3 becomes -3 (2x + 1)
See how the (2x + 1) is the common factorization? So that is one term and what is left, the 2x-3 is the other.
Don't forget your 4, the final answer is:
4(2x+1)(2x-3)
foil it back out to be sure!
4(4x^2-6x+2x-3)
4(4x^2-4x-3)
16x^2-16x-12
Looks good
All the best
Lori
Craig T.
11/27/16