       Re: factoring quartic over radicals

• To: mathgroup at smc.vnet.net
• Subject: [mg37079] Re: [mg37006] factoring quartic over radicals
• From: "German BUITRAGO A." <gerbual at col2.telecom.com.co>
• Date: Tue, 8 Oct 2002 07:17:46 -0400 (EDT)
• References: <200210060932.FAA27437@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hello, Steve:

The key is in using the command Factor with the option Extension:

In:=
Factor[x^4 + x^3 + x^2 + x + 1, Extension ->  {GoldenRatio}]

Out=
-((-1 - x + GoldenRatio*x - x^2)*(1 + GoldenRatio*x + x^2))

For manual verification you should keep in mind that:

1/GoldenRatio = GoldenRatio - 1

Best regards,

Germán Buitrago

----- Original Message -----
From: "Steve Earth" <SteveE at harker.org>
To: mathgroup at smc.vnet.net
Subject: [mg37079] [mg37006] factoring quartic over radicals

> Greetings MathGroup,
>
> My name is Steve Earth, and I am a new subscriber to this list and also a
> new user of Mathematica; so please forgive this rather simple question...
>
> I would like to enter the quartic x^4 + x^3 + x^2 + x + 1 into Mathematica
> and have it be able to tell me that it factors into
>
> (x^2 + GoldenRatio x + 1) ( x^2 - 1/GoldenRatio x + 1)
>
> What instructions do I need to execute to achieve this output?
>
> -Steve Earth
> Harker School
> http://www.harker.org/
>

```

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