       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)
>