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Factoring a Trinomial


Date: 08/26/97 at 18:37:04
From: beth phillips
Subject: Intermediate algebra

     5k^2 - 13k - 6
     --------------
         5k + 2

How do you reduce this to lowest terms?


Date: 08/30/97 at 08:48:23
From: Doctor Anthony
Subject: Re: Intermediate algebra

They require you to factorize 5k^2 - 13k - 6.

Factorizing trinomials cannot always be done, but in this case 

        5k^2 - 13k - 6 =  (5k + 2)(k - 3)

This gives you a common factor of (5k + 2) in the numerator and denominator, which you can cancel to simplify the expression. 

How do we do this factoring into binomials?
                            
Looking at the right hand side, the terms 5k and k combine to give 
5k^2. The terms 2 and -3 combine to give -6. The two outer terms 
5k and -3 give -15k and the two inner terms 2 and k give 2k.  
Combining these two k terms we get -13k as required.

The sequence when factorizing a trinomial is:

Look at the term in k^2, and consider possible factors. In this case 
the only possibilities are 5k and k, so put 5k in the first bracket on 
the right and k in the second bracket on the right.

Look at the constant term -6. Possible factors are 

  3, -2,  
 -3, 2, 
  6, -1  or 
 -6, 1.  

You will need to put one of the pair in each bracket, so we must 
decide which pair to use and into which bracket the individual members 
of the pair must go.  To do this we look at the term in k, -13k.

-13k = -15k + 2k, so we see how to get -15k and how to get 2k.  By 
putting -3 in the second bracket and 2 in the first bracket we achieve 
the result we want.

You will notice that there is an element of trial and error in the 
process of factorizing, but with practice it can be done quickly.  
I would advise you to get a textbook with many examples and work your 
way through as many of those as you can.

-Doctor Anthony,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Basic Algebra
High School Polynomials
Middle School Algebra
Middle School Factoring Expressions

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