Find a Pair of Factors of AC Whose Sum is B

Date: 04/12/2002 at 00:08:38
From: Robert Draper
Subject: A C bust B? factoring

When I was a freshman, I was taught a method called either A B Bust C 
or A C Bust B. Over the years, my memory of this method has faded and 
I do not remember exactly how to do it. Do you have any knowledge of 
this method? 

Thank you.    
Robert

Date: 04/12/2002 at 12:05:49
From: Doctor Peterson
Subject: Re: A C bust B? factoring

Hi, Robert.

I wonder if the "AC method" discussed here might be what you have in 
mind:

   A C Method - Student Learning Assistance Center,
     Southwest Texas State University 
   http://www.swt.edu/slac/math/ACMethod.html 

   Factoring Trinomials - Dr. Math archives
   http://mathforum.org/library/drmath/view/56442.html 

The idea (which is worded a little oddly in the first, and hidden in 
the middle of the second) is to find a pair of factors of AC whose sum 
is B. For example, to factor 6x^2 + 25x - 9, AC = 54 = -2*3*3*3, and 
if we choose AC = -2*27, the sum of the factors is 25. Then we write 
it as

    6x^2 + 27x - 2x - 9

and factor by grouping:

    3x(2x + 9) - (2x + 9)

    (3x - 1)(2x + 9)

I agree that this is a lot easier than the method I learned.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/