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MathGroup Archive 2002

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Re: Re: Factoring question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg35470] Re: [mg35458] Re: Factoring question
  • From: Ken Levasseur <Kenneth_Levasseur at uml.edu>
  • Date: Sun, 14 Jul 2002 06:19:43 -0400 (EDT)
  • References: <agbfhl$je9$1@smc.vnet.net> <200207130748.DAA08575@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Steve:

I assume that the problem was  to solve x^7 + x^5 + x^4 + -x^3 + x + 1=0.  If
so, one of the basic factoring theorems is that if a polynomial over the
integers  like this one has a rational root r/s, then r must divide the
constant term and s must divide the leading coefficient.   So in this problem,
+/-1 are the only possible rational roots and so the (x+1) factor would be
found this way.   I'm sure that Mathematica checks this almost immediately.
As for the remaining 6th degree factor, I'm not certain how Mathematica
proceeds, but if you plot it, it clearly has no linear factors.

Ken Levasseur


Steven Hodgen wrote:

> "DrBob" <majort at cox-internet.com> wrote in message
> news:agbfhl$je9$1 at smc.vnet.net...
> > Factor[x^7 + x^5 + x^4 + -x^3 + x + 1] // Trace
>
> This doesn't do it.  It only traces the initial evaluation, and then simply
> displays the factored result with no intermediate factoring steps.
>
> Thanks for the suggestion though.
>
> >
> > Bobby
> >
> > -----Original Message-----
> > From: Steven Hodgen [mailto:shodgen at mindspring.com]
To: mathgroup at smc.vnet.net
> To: mathgroup at smc.vnet.net
> > Subject: [mg35470] [mg35458]  Factoring question
> >
> > Hello,
> >
> > I just purchased Mathematica 4.1.  I'm taking precalculus and wanted to
> try
> > a tough factoring problem, since the teacher couldn't do it either.
> > Mathematica get's the correct answer, but I'm interrested in seeing how it
> > got there.  Is there a way to turn on some sort of trace feature where it
> > shows each step it used to get the the final result?
> >
> > Thanks!
> >
> > --Steven
> >
> >
> >
> >
> >
> >
> >



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