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MathGroup Archive 2005

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Re: silly questions?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg59061] Re: silly questions?
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Thu, 28 Jul 2005 02:26:05 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, U.K.
  • References: <dc77me$k74$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Kent Holing wrote:
> Why does not (x^5-32)/(x-2)//FullSimplify in Mathematica  work?
> Compare with Factor[x^5-32]//InputForm which returns (-2 + x)*(16 + 8*x + 4*x^2 + 2*x^3 + x^4).
> So why does not the first command just return 16 + 8*x + 4*x^2 + 2*x^3 + x^4?
> As in a factorization above, how is the easiest way to pick automatically (by a function) the factors of say degree >=2,  if any ?
> 
> Kent Holing
> 
Hi Kent,

It occurs that *Simplify* or *FullSimplify* are not designed to do what 
you have in mind. Try *Factor* instead:

In[1]:=
expr = (x^5 - 32)/(x - 2)

Out[1]=
(-32 + x^5)/(-2 + x)

In[2]:=
Factor[expr]

Out[2]=
16 + 8*x + 4*x^2 + 2*x^3 + x^4

For your second question, have a look at the function *FactorList*

http://documents.wolfram.com/mathematica/functions/FactorList

You can extract the factors with a power greater or equal to 2 as in the 
following example:

In[3]:=
fl = FactorList[64 - 12*x^2 + 2*x^3]

Out[3]=
{{2, 1}, {-4 + x, 2}, {2 + x, 1}}

In[4]:=
Select[fl, #1[[2]] >= 2 & ]

Out[4]=
{{-4 + x, 2}}

Best regards,
/J.M.


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