I'm not sure what you mean by "through factoring, becoming"...? Are you perhaps asking for the Greatest Common Factors of each pair of terms?
(The link you list relates to a very different topic.)
Thank you! :D
Yes stapel, it's most probably the greatest common factors..
Apr 20th 2009, 02:49 AM
more specifically, why is the GCF of -16x and 12 -4 and not 4? The GCF of -3x and 12 -3 and not 3? And the GCF of 4x^2 and -16x 4 and not -4??
Apr 20th 2009, 03:29 AM
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.
Apr 20th 2009, 03:49 AM
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