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MathGroup Archive 1995

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Re: [Q] Factor

  • To: mathgroup at christensen.cybernetics.net
  • Subject: [mg1288] Re: [Q] Factor
  • From: wagner at bullwinkle.cs.Colorado.EDU (Dave Wagner)
  • Date: Wed, 31 May 1995 05:45:48 -0400
  • Organization: University of Colorado, Boulder

In article <3qdsb3$454 at news0.cybernetics.net>,
Bernd Last <blast at bendix.swb.de> wrote:
>If I have a funktion like:
>
>f[x_] = (a + b x + c x^2) (2x - 2x^2)
>
>
>How can I factor it like that?
>
>f[x_] = a (2x-2x^2) + b x (2x-2x^2) + c x^2 (2x-2x^2) 
>          \_______/     \_________/     \___________/  
>              I              II              III
>
>And how can I get those factors?
>
>I    -> (2x-2x^2)
>II   -> x (2x-2x^2)
>III  -> x^2 (2x-2x^2)

I suspect the example given is a very simple example of a more general
problem, so I don't know if the following will help or not:

    f = (a + b x + c x^2) (2x - 2x^2)
	      2                2
    (2 x - 2 x ) (a + b x + c x )

    % /. 2x-2x^2->y
		  2
    (a + b x + c x ) y

    Expand[%]
		     2
    a y + b x y + c x  y

    % /. y->2x-2x^2
		2                  2       2           2
    a (2 x - 2 x ) + b x (2 x - 2 x ) + c x  (2 x - 2 x )

    Coefficient[%, a]
	     2
    2 x - 2 x

		Dave Wagner
		Principia Consulting
		(303) 786-8371
		dbwagner at princon.com
		http://www.princon.com/princon


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