Question 799755: Im having trouble on factoring. The problem is 20a^3+37a^2+8a. I pulled out an a as the greatest common factor and now have a(20a^2+37a+8). But now im stuck. is this where I do the product and some? I just don't know where to go from her.
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! You are correct to take out the common factor of a. This gives you
a(20a^2+37a+8), which you have. The next step is to factor the trinomial. I call this "Advanced Trinomial Factoring," and I have a detailed explanation on my website that you may want to see. First however, I'll try to explain your problem for you. You need to "undo" the trinomial by "un-FOILing" it, if you know what I mean. You need to break down the 20a^2 into a product that will be the "First" times "First":
( a+___ )(20a+___ )
(2a+___ )(10a+___ ) or
(5a+___ )(4a+___ )
Meanwhile the Last times Last has to end up with a product of 8:
(___+ 8)(___+ 1)
(___+ 1)(___+ 8)
(___+ 2)( ___+4)
(___+ 4)(___+ 2)
Most importantly, the middle term has to add up to 37a. There are often a LOT of different combinations to try to see which one works. However, there are usually some short cuts too!! In this case, a really GOOD shortcut is that the middle term 37a is an ODD number, so you CANNOT use any EVEN-EVEN combinations. This means that it HAS to be 5a*4 or 20a*a. Also, it HAS to be 1*8 or 8*1 for the last times last.
It turns out that the winning combination is (5a+8)(4a+1), since the middle term 5a + 32a adds up to 37a. Final answer is a(5a+8)(4a+1).
Please see also my website by using the easy-to-spell and easy-to-remember link www.mathinlivingcolor.com. Click the link at the bottom of the page which takes you to my Homepage. On the Homepage, look for the link near the top of the page "Basic Algebra: One Step at a Time." Look in "Chapter 2" for the section called "Advanced Trinomial Factoring". There you will find a much more detailed explanation of the topic, with lots of examples and exercises, with many of the exercises solved IN COLOR on the corresponding "Math in Living Color" pages. The website has detailed explanation for most topics in algebra, explained especially for students who have trouble understanding their traditional textbooks! If you like the website, please recommend it to your friends and family who have trouble with math!
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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