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Question 312882: Why is (3x + 5) (x - 2) + (2x - 3) (x - 2) not in factored form? What is the correct final factored form? What is this factoring method called?
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! To factor means to express as a product. The expression that you gave is NOT factored because it is NOT a product. To express it in factored form, you have to take out a COMMON FACTOR OF (x-2). In this way it becomes:
(3x + 5) (x - 2) + (2x - 3) (x - 2)
(x - 2) ( (3x+5) + (2x - 3) )
Now you can combine like terms in the second quantity:
(x-2)(5x+2)
For additional help with a variety of topics on FACTORING, please see own my website by clicking on my tutor name "Rapaljer" anywhere in algebra.com. Then click on the link there to my website. From my Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Look for "Basic Algebra" and look in Chapter 2. There are several sections that relate to factoring. This is FULL of examples, exercises, and answers to all the exercises. See also the "Math in Living Color" pages where many of these exercises are solved IN COLOR. My own students used to tell me that my explanations are much easier to understand than the traditional textbooks. Perhaps you will like this section.
I also have a video (actually 2 videos!) on the topic of FACTORING. To see the videos, which by the way are FREE, from my Homepage, look for the link "Rapalje Videos in Living Color." Choose either "Basic Algebra" or "Intermediate Algebra", depending upon your level of algebra skills.
I just want to make math easier for people who have trouble with math. It's usually not as hard as everyone thinks it is. The website has a lot of resources--all FREE.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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