SOLUTION: Factor the expression: 2x^2 + 5x + 3

Question 596701: Factor the expression: 2x^2 + 5x + 3

Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
I call this "Advanced Trinomial Factoring", and I have an entire section explaining it on my website. I'll give you more on that later. For now, here is your solution.

2x^2 + 5x + 3

You need to start out with the First times First like this:
(2x+___)(x+____)

Then, the Last times Last has to be 3, which is either 3*1 or 1*3. The trick is that the MIDDLE term has to add up to 5x. By trial and error,

(2x+3)(x+1) is the final answer, since OUTER times OUTER is 2x, INNER times INNER is 3x, which adds up to 5x.

For additional explanation on FACTORING, in particular "Advanced Trinomial Factoring", please see my own website. The easiest way to find it is to use the easy to spell and easy to remember link www.mathinlivingcolor.com. On this single page website, there is a link at the bottom of the page that takes you to my Homepage.

Near the top of my homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time", and choose Basic Algebra (Chapter 2), Section 2.06. There you will find explanations that may be easier to understand than your traditional textbooks, and many of the exercises from these sections are solved in color on the "MATH IN LIVING COLOR" pages that go with these sections.

There are also VIDEOS of me teaching this topic a few years before I retired. There is a video on FACTORING in Basic Algebra, and also in Intermediate Algebra. As I recall, there is more explanation of Advanced Trinomial Factoring in the Intermediate Algebra video. These videos are FREE, and you can see them by looking on my Homepage for the link "Rapalje Videos in Living Color."

If you like my website, please tell your friends and family. It's all FREE. You can contact me by Email at rapaljer@seminolestate.edu.

Dr. Robert J. Rapalje, Retired
Professor of Mathematics
Seminole State College of Florida
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