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Get the factorization of a polynomial?

Posted 2 months ago
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Hello. I have already asked for help in this forum and I thank those who replied but I still can't factor the polynomial a^2-3b^2. The "Factor" command factors it in Q but not in the set R. Is it a software problem or, more likely, something escapes me? I tried to add the "Extension-> Automatic" command but it does not recognize it and the online manual did not help me. Thanks for the help you want to give me.

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The Extension->Automatic does not work. I hope this will improve in later versions. You can give the extension manually:

Factor[a^2 - 3 b^2, Extension -> Sqrt[3]]

or have it computed by Mathematica itself:

pol = a^2 - 3 b^2;
Factor[pol,
 Extension -> Cases[Solve[pol == 0],
   _?NumericQ, All]]

Many thanks for the reply. Unfortunately, if I want to use it in class I have to assume that students see sqrt (3)

I tried but it does not work. Returns the attached screen

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Enter the Wolfram Cloud and try the code in there.

The result I sent it gives by Wolfram Cloud. The desktop version answers "Wolfram Alpha doesn't know how to interpret your input".

Actually, if factoring a^2-3, gives me the correct result in R but as soon as I put b ^ 2 (a^2-3b^2) it doesn't factor it in R set. It seems not to recognize the second variable.

It works for me on the Wolfram Cloud.

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I can't understand. Thanks anyway.

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