How to factor a polynomial modulo p?

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Is there a general strategy to factoring a polynomial modulo p? I've looked on Google but I've had a hard time finding anything that specifically outlines an approach that I can understand.

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Yes, there is for instance Berlekamp's algorithm, which I discussed in some detail in this answer.

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Yes, there is. Refer to these links, there's a clear description on how modulo primes determine the factorization of polynomials.

Elementary properties of polynomials

Integer Polynomials