🚀 go-pugleaf

I am curious why we even bother to teach factoring over the rationals.
What Murphy says is correct yet most students of algebra leave their
courses feeling that all polynomials should be factorable with at least
one rational factor. It is never mentioned in most texts that the reason
we give one zero of a cubic is that we could not factor the remaining
quadratic if it were not for the quadratic formula. Are we guilty of
fruad? I would like to see the algebra curriculum address the fact that
the real world is better modeled by discrete dynamical systems and focus
more attention on understanding numerical techniques.

Peolpe who voice concerns about "Black Box" mathematics have some
validity thier argument(yet they still teach the long division algoritm
without explaination). We are at a dangerious point in the
evolution of our technology with linkable calculators. Students should be
introduced to more of the math behind the "Box." I would rather teach the
bisection method in elementary algebra than factoring over the integers
for ten different special cases. I'd wager money they'd remember the
bisection routine before how to factor using the ac method.

On Tue, 6 Dec 1994, DAVE_LUNSFORD wrote:

>
> On 12/4/94 Murphy Waggoner posted:
>
> >In fact, there is zero probability that the cubic formula
> >implemented properly on a computer will give exact results,
> >because the probability that the solutions will be irrational is
> >100%.
>
> Any cubic polynomial factorable over the rationals will yield at
> least one linear factor with a rational zero.  There could be as
> many as three rational zeros and the formula should find them as
> exact roots.
>
> Dave Lunsford
> Grossmont College
>
> dave_lunsford@gcccd.cc.ca.us
>
>
>