One can easily factor a polynomial over finite fields of prime order, using Factor command:

Factor[1 + x^2, Modulus -> 2]
===>  (1 + x)^2

Now, is it possible to do this over finite fields of non-prime order? As an example, $ x^2 + x + 1$ is reducible over GF(4), and can be decomposed as $(x-a)(x-a^2)$, where $a\not\in \{0,1\} $ is a field member.

Problem is, members of non-prime order finite fields are not denoted by ordinary numbers; rather, they use either polynomial or vector notation.



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