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Re: factoring quartic over radicals


In a message dated 10/6/2002 6:31:10 AM, SteveE at harker.org writes:

>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?
>

soln = Factor[x^4 + x^3 + x^2 + x + 1,
      Extension -> GoldenRatio] // Simplify

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

soln = Simplify /@ 
    (soln /. -GoldenRatio -> -1 - 1/GoldenRatio)

(x^2 - x/GoldenRatio + 1)*(x^2 + GoldenRatio*x + 1)

soln // FunctionExpand // FullSimplify

x^4 + x^3 + x^2 + x + 1


Bob Hanlon


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