why would 4x^2 and -3x through factoring become x,
-16x and +12 become -4
4x^2 and -16x become 4x
What's this procedure called and how does one procede? This site Factoring Quadratics: The Hard Case about factoring quadratics doesn't tell.. Thanks
You have to compare the terms to check if is there is something that is commun to both of them. Por example, you can check if they are divisible by x or by 4 ... and so on.
Check this website: Factoring: Some Special Cases
They're probably trying to "clean up" the result. That is, they're trying to order the terms in the result, and try and make the first term positive. Polynomials are usually arranged with the term with the highest degree first, and it's sort of traditional to try and make the first term positive.
So if I want to factor something like -16x + 12, I might want to do so as -4(4x - 3) rather than 4(-4x + 3) because (4x - 3) is "cleaner" than (-4x + 3).
That's my take, it's sort of hard to explain, but both are technically correct IMO. I'm liable to factor it which ever way makes my life easier, depending on context. Otherwise I do as I said and try and make the first (highest degree) term positive.
Someone correct me if I'm wrong, but it seems an aesthetic choice to me.
HOWEVER, GCF is technically the *greatest* common factor. If I wanted to be pedantic, I think I could say that the positive factor is greater than the negative one, and thus the positive one is the correct answer. Frankly, I wouldn't worry about it. If you have a teacher, do it however they say, of course.
Hope that's not as confusing as I suspect it may be. Long story short, don't worry too much about it.
Yeah in this case it does make sense if it's plus or minus because what I'm originally trying to do is to factor a hard quadratic, in this case 4x^2 – 19x + 12. Which is
(x–4)(4x–3) but couldn't be (x+4)(4x+3). Again, this is the page that shows how it's done Factoring Quadratics: The Hard Case