Splitting Fields - Abstract Algebra

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Question

What definition does the following correlate to?

If is a prime, then the following polynomial is irreducible over the field of rational numbers.

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Answer

The Eisenstein's Irreducibility Criterion is the theorem for which the given statement is a corollary to.

The Eisenstein's Irreducibility Criterion is as follows.

is a polynomial with coefficients that are integers. If there is a prime number that satisfy the following,

Then over the field of rational numbers is said to be irreducible.

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