Re: [Q] Factor
- To: mathgroup at christensen.cybernetics.net
- Subject: [mg1290] Re: [Q] Factor
- From: bob Hanlon <hanlon at pafosu2.hq.af.mil>
- Date: Wed, 31 May 1995 06:05:49 -0400
f[x_] = (a + b x + c x^2) (2x - 2x^2);
Treat the polynomial in x as if it were a polynomial in a, b, or c.
Generate the coefficients and keep only the first order term:
Last[CoefficientList[f[x], #]]& /@ {a, b, c}
2 2 3 3 4
{2 x - 2 x , 2 x - 2 x , 2 x - 2 x }
Factoring does not produce the exact form requested:
Factor[Last[CoefficientList[f[x], #]]]& /@ {a, b, c}
2 3
{2 (1 - x) x, 2 (1 - x) x , 2 (1 - x) x }
Dividing by the desired factor produces the required "coefficients":
Cancel[(Last[CoefficientList[f[x], #]]& /@
{a, b, c})/(2x - 2x^2)]
2
{1, x, x }
Reintroducing the factor provides the required form of the factors
for a, b, and c:
Cancel[(Last[CoefficientList[f[x], #]]& /@
{a, b, c})/(2x - 2x^2)] (2x - 2x^2)
2 2 2 2
{2 x - 2 x , x (2 x - 2 x ), x (2 x - 2 x )}
Bob Hanlon
> From: blast at bendix.swb.de (Bernd Last)
> Newsgroups: comp.soft-sys.math.mathematica
> Subject: [Q] Factor
> Date: 30 May 1995 01:28:03 GMT
>
> 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)
>
> Answers are greatly appreciated.
>
> Bernd