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### 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/
```
Associated Topics:
Middle School Factoring Expressions

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