If you are concerned with factoring a polynomial, Factor is the appropriate command:

If you would like to specify an extension in which to factor, say one with , use the Extension option:

If you would like to specify a modulus for the factorization, like 3, use the use the Modulus option:

For a polynomial of multiple variables, Factor will still try to decompose it:

Sometimes, the factors themselves are not of interest so much as whether or not the polynomial itself is irreducible. You can find this information using IrreduciblePolynomialQ, let us try it on :

To get the largest factor of a collection of polynomials, say , use the PolynomialGCD command:

A univariate polynomial can always be factored into linear factors by finding all of its roots: