RE: factoring quartic over radicals

*To*: mathgroup at smc.vnet.net*Subject*: [mg37048] RE: [mg37006] factoring quartic over radicals*From*: "DrBob" <drbob at bigfoot.com>*Date*: Mon, 7 Oct 2002 05:25:03 -0400 (EDT)*Reply-to*: <drbob at bigfoot.com>*Sender*: owner-wri-mathgroup at wolfram.com

It's a little ugly, but here's my solution: x^4 + x^3 + x^2 + x + 1 Simplify@Factor[%, Extension -> {GoldenRatio, 1/GoldenRatio}] Collect[%[[2]]/3, x]Collect[%[[3]]/3, x] % /. Sqrt[5] -> 2GoldenRatio - 1 % // Simplify Collect[#, x] & /@ % % /. {1 - GoldenRatio -> -1/GoldenRatio} FullSimplify@Expand@% (The last line is a check.) Bobby -----Original Message----- From: Steve Earth [mailto:SteveE at harker.org] To: mathgroup at smc.vnet.net Subject: [mg37048] [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/