Question 328707
-30w^2+w+1
-1(30w^2-w-1)


Now, this is a factorable trinomial.  You need to find two numbers whose product is 30w^2 (probably 6w*5w) like this:
-1(6w____)(5w_____)



The last times last must come out to -1, so it must be either -1*1 or 1*-1.  The combination that works to give you a -w for the middle term (by trial and error!) is
-1(6w+1)(5w-1)


Now it just so happens that FACTORING, especially factoring the common factor, is one of my FAVORITE kinds of problems!  I have a COMPLETE explanation of this topic, in my own curriculum that I'm giving away FREE on my own website!  To see this website, click on my tutor name "rapaljer" anywhere in algebra.com.  Click on my website name that you will see there, and look on my Homepage for "Basic, Intermediate, and College Algebra: One Step at a Time."  Choose "Basic Algebra" and look in "Chapter 2" for the appropriate topics.  There are about 6 sections that deal with each of the different types of factoring that I explained there.  Look for the section called "Advanced Trinomial Factoring."  These are my own explanations that are written especially for students who have trouble with math!  


In addition, many of my exercises are solved in my "Math in Living Color" pages that accompany each of these sections.


Not only do I have a complete written explanation for this topic, I also have a video that was made a few years before I retired.  The videos are also FREE, and you can see the videos by looking on my Homepage for "Rapalje Videos in Living Color."  From here, choose "Basic Algebra" and look for the video on Factoring.  You may need to download RealPlayer, if you do not have it already on your computer, but this too is a free download.  And, you don't have to watch the whole video, but I have indicated on the video pages where to look for each particular type of factoring problem.  


I hope you like my curriculum and my videos.  I have other topics as well.  When I was teaching, my own students were unanimous that my explanations were a LOT easier to understand than the traditional textbooks.  If you like it, please recommend it to your family and friends who need help with math!!  Like algebra.com, it's all FREE!!


Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus