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 Subject: RE: Conceptual approach to factoring polynomials Author: Mathman Date: Dec 6 2006
On Dec  6 2006, UtahDonut wrote:
> I would like to know if anybody is familiar with a conceptual
> approach to factoring polynomials that is effective.

What do you mean by "conceptual"? Is that just another way of saying that is
must apply to "the real world"?  Also, which sort of polynomials? a leading
coefficient of 1, or more general?  I have passed along to some teachers a
"method" of solving the more general problem which they found to be effective
where other methods failed.  However, I doubt you'd think it to be "conceptal",
or intuitive in any sense by itself, although based upon a firm academic
argument.

I, and any I've been in contact with, usually lead up to such studies using
number systems, the main concept being that factoring is an inverse operation to
the multiplication of factors.  In that sense, it is a method of finding prime
elements.  Usually, such studies are built over a period of time with several
considerations, and not just a single lesson plan.  When the idea of prime
factors in numbers and their application to techniques in arithmetic is grasped,
that leads to factoring of polynomials, which are really a generalise number
system.  The results are then applied to larger number systems, as in radicals,
then complex numbers, and so on.  It's an entire process and development that
has been going on for some time.

David.