Question 567805: factor 7p^2 +33p -54 how would you factor?
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! 7p^2+33p-54
The only way to get the FIRST term 7p^2 is to use 7p*p:
(7p_____)(p_______).
Next, look at the LAST term, which is -54. The sign is negative, so you need to find the product of two numbers with OPPOSITE sign. You can get all the combinations for 54 by starting with 1*54 and continuing as follows:
1*54
2*27
3*18
6*9
Since the last term is NEGATIVE, you have to use the opposite signs in such a way that the MIDDLE term comes up with a DIFFERENCE of 33. The middle term must be such that 7 times one of the numbers MINUS the other number is 33.
Notice that in the last combination of numbers above 6*9, multiply 7*6 and subtract 9, and you get 33. The solution looks like this:
(7p____)(p_____)
(7p___9)(p___6) The OUTER times OUTER is 42p. The INNER times INNER is 9p.
(7p - 9)(p + 6) The OUTER times OUTER is +42p. The INNER times INNER is -9p, for a total of +33p.
For a complete explanation of this and other topics in FACTORING, please see my own website. The best way to find it is to use the easy-to-remember and easy-to-spell link www.mathinlivingcolor.com. At the bottom of the page there is a single link that takes you to my Homepage. On my Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "Basic Algebra", and look in "Chapter 2" for "Section 2.06 Advanced Trinomial Factoring." Here you will find my own non-traditional explanation that my own students used to find much easier to understand than most of the other textbooks being used. I also have lots of examples, exercises, and answers. In addition, most of the hardest problems are solved in color on the MATH IN LIVING COLOR pages that go with this topic. There is a VIDEO of me teaching FACTORING in class before I retired a few years ago. To find the video, look on my Homepage for "Rapalje Videos in Living Color," choose "Basic Algebra" and select the "Factoring" video. It's ALL FREE on my website!!!
To contact me please use my Email address at rapaljer@seminolestate.edu.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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