Re: Re: Factoring question

• To: mathgroup at smc.vnet.net
• Subject: [mg35485] Re: Re: Factoring question
• From: "Steven Hodgen" <shodgen at mindspring.com>
• Date: Tue, 16 Jul 2002 04:49:44 -0400 (EDT)
• References: <agbfhl\$je9\$1@smc.vnet.net> <200207130748.DAA08575@smc.vnet.net> <agrjfj\$g9n\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Actually, I never posted the actual problem, but here it is:

y^4 - (p + q)*y^3 + (p^2*q + p*q^2)*y - p^2*q^2

This factors to:

(y^2 - p*q)*(y - p)*(y - q)

Which I cannot get.  I've tried over an over again, and I'm the best
factorer in my class, my instructor can't seem to get this either, hence my
hope that Mathematica could do it, and it certainly can no problem, but it
just doesn't show how.  So, any ideas?

--Steven

"Ken Levasseur" <Kenneth_Levasseur at uml.edu> wrote in message
news:agrjfj\$g9n\$1 at smc.vnet.net...
> 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
> > > Subject: [mg35485]   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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