Q&A #18119

Teachers' Lounge Discussion: "Bottoms up" as a method to factor trinomials

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From: Wes Bruning <firmeadow@bctonline.com>
To: Teacher2Teacher Public Discussion
Date: 2008050100:01:51
Subject: "Bottoms up" factoring trinomials

I have been teaching this method of factoring trinomials for a number
of years. It is commonly referred to as the "ac method" due to mn=ac
step. A number of texts include it. My school has chosen to include it
in the 2nd Algebra term.

However, I do not recommend it to students. Actually, I discourage its

The ac method us useful for trinomials that have something other than
a 1 for the x^2 term and have multiple factors for both a and c (ax^2
+ bx + c). This can be a tough factorization problem.

BUT, the problem is that one has to be able to guess a pair or numbers
(m and n) that when multiplied equal ac and when added equal b. How
often does this occur? Never outside of the math classroom. If m or n
is not a whole number they cannot be guessed. The method is so
restrictive it is worthless. At best it is a time wasting method
requiring the student to memorize a set of procedures they will never
use outside of that particular math class.

If one is to spend time learning a procedure-based method of
factoring, spend the time on the quadratic formula. The quadratic
formula is a tool that works every time and all the time. It is used
in many advanced math solutions both theoretical math and practical
math. It is used in engineering and other sciences.

Spend your time and your student's time and efforts on something with
lasting value. The ac method is not it.

Wes Bruning
Oregon City, OR

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