> Why are they called The FUNDAMENTAL Theorem of Arithmetic and The
> FUNDAMENTAL Theorem of Algebra? :-)
>
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Actually, the fundamental theory of Algebra has more to do with identifying
roots of polynomial functions then it does with finding factors (linear or
otherwise). Papa Abel showed us all that no algorithm exists for finding roots
(and thus factors) for generalized polynomials above degree 4 (actually you can
do degree 5 if you have some background in elliptic curves). In physics and
most other applications, the most important goal is for a student to be able to
identify and classify roots. So perhaps we should spend more time teaching them
numerical techniques for approximating roots.
Jay Malmstrom
Oklahoma City Community College
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