The Best Way to Factor Trinomials – A Remarkable Coincidence

I first got the idea for the “best” factoring method when I was looking at stretching the number line to make rational polynomial roots into integers, but if a person solves enough quadratic equations by factoring, the pattern will become apparent.  I was sure that the method was not new.  I called it the “best method” to be emphatic and to get a little attention.  I did a desultory search for antecedents and found a few but no full-blown exposition.

Yesterday I was installing Wolfram’s CDF player on my tablet for a demonstration in Precalculus II and started to get antsy.  There is a table outside my office and someone had put out something like seventy old math magazines, free for the taking.  I picked up the magazine closest to hand, Mathematics Teacher, volume 83, number 8, November 1990.  I was idly paging through back to front chuckling at the primitive BASIC computer programming code when suddenly my eye caught a letter to the editor from Warren A. Groskeutz, a high school teacher in Glendale, Wisconsin.  He stated that his student, David Barson, had discovered a quick way to solve quadratic equations – precisely the method I have described in the last few posts.

I am a logical, rational individual who supposedly understands probability, but I couldn’t help but be amazed that that one magazine and that one page would come to hand at the exact time that I was thinking about the issue.  A part of me wanted to believe that mysterious forces were at work.  The other part was saying to me that a very low probability event had occurred and so what.  In any case, I am richer and humbler for the experience and have yet another  reason to marvel at the processes of the universe – random or not.


About jrh794

I am a sixty-five year old math instructor at Southern Oregon University. I taught at the College of the Siskiyous in Weed California for twenty-six years. Prior to that I worked as a computer programmer, carpenter and in various other jobs. I graduated from Rice University in 1967 and have a MS in Operations Research from Stanford. In the past I have hand-built a stone house and taken long solo bicycle tours. Now I ride my mountain bike and play golf for recreation.
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One Response to The Best Way to Factor Trinomials – A Remarkable Coincidence

  1. Anonymous says:

    My 6th grader would say, “Wow! That’s so random!”. My 4th grader appreciates your crisscross applesauce post. I saw it on Pinterest. Thanks!

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