Question 313881: factorise 21xsquared -20x-1
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! Factor: 
I call this "Advanced Trinomial Factoring" since it is a trinomial where the coefficient of  is larger than 1. For a full explanation of my method, please see my own website, using the information I will give after I solve this problem for you.
You know the answer to this, if indeed it can be factored, will be the product of two binomials, like this:
( _____ )( _____ )
The FIRST term times the FIRST term must give you 21x^2, so it will be either
(7x_____)(3x_____) OR (21x_____)(x_____)
It turns out that the second combination works better than the first one, since the middle term is -20x. Now, the LAST times LAST term must be -1, so let's try this:
(21x+1)(x-1) OR (21x-1)(x+1)
In this case, the FIRST choice works out to give you a middle term of -21x+1x=-20x. This is correct, so this is your final answer:
(21x+1)(x-1)
Now, for additional help with FACTORING, please see my own website. Click on my tutor name "rapaljer" anywhere in algebra.com. There you will see the link to my Homepage. Near the top of my Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "Basic Algebra", and look for "Chapter 2." See Section 2.06, Advanced Trinomial Factoring for more explanataion on this particular type of problem. If you need help with other types of factoring, see the other sections in this chapter. Here, you will find my own non-traditional explanation of FACTORING, complete with examples, exercises, and ALL the answers. Many of these exercises are also solved IN COLOR on my "Math in Living Color" pages that go along with these sections.
In addition, please see my FREE videos, which were make from my own classes before I retired a few years ago. From my Homepage, look for the link "Rapalje Videos in Living Color", choose "Basic Algebra" and look for the topic on "Factoring". I hope this will be helpful, and that my explanation is easier to understand than the traditional textbooks.
Also, my Email address is at the bottom of each page of my website. I'll be glad to help if I can.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
|
|
|
