Question 227598: In my (online) math class we were learning about factoring trinomials completely and factoring out the opposite gcf when they gave me this equation:
-12x^3+14x+10x
-12x^3 obviously means I need to find a gcf, but if I did that I'd take away the x from the 14, which then it would be ax^2+b+c when it should be ax^2+bx+c
Could you PLEASE help me? Im confused
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! The first step is to take out the COMMON FACTORS. I think this is what you call the gcf. In this case, you have a common factor of 2 and x, so take out the 2x. Also, I suspect that you may have meant this to be 14x^2 for the middle term, am I right? If so, do this:
-12x^3 + 14x^2 + 10x
2x(-6x^2 + 7x + 5)
They may also have meant for you to take out a common factor of -2x:
-2x(6x^2 - 7x -5)
You really need to see my Lessons on Factoring, especially the ones on FACTORING THE COMMON FACTOR and FACTORING TRINOMIALS. Go to my own website by doing a "Bing" or "Google" search for my last name "Rapalje". Look for and click on "Rapalje Homepage" at or near the top of the search results. Near the top of my Homepage, look for "Basic, Intermediate and College Algebra: One Step at a Time." Select "Basic Algebra" and look in Chapter 2, for several sections related to "Factoring." I also have lots of problems solved in my "MATH IN LIVING COLOR" pages that correspond to these sections. One final resource that I have are FREE videos of me teaching this in my own classroom a few years ago. To see my videos, go back to my homepage, and look for "Rapalje Videos". Look in "Basic Algebra" for the topic "Factoring." This is all free.
R^2
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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