# irreducibility using factor function()

Consider the polynomial p=x^3-3*x+4. Use the factor() function to determine if p is irreducible over:

irreducibility using factor function()

Consider the polynomial p=x^3-3*x+4. Use the factor() function to determine if p is irreducible over:

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answered 2017-10-11 07:48:46 +0200 **

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sage: R.<x> = IntegerModRing(5)[] sage: k = x^3 -3*x + 4 sage: K = k.factor(); K sage: k.is_irreducible()

sage: R.<x> = CC[] sage: p = x^3 -3*x + 4 sage: P = p.factor(); P sage: p.is_irreducible()

sage: R.<x> = CC[] sage: p = x^3 -3*x + 4 sage: P = p.factor(); P sage: p.is_irreducible()

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Asked: ** 2017-10-08 00:27:24 +0200 **

Seen: **305 times**

Last updated: **Oct 08 '17**

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This looks like homework. Please always mention the own effort to make sage compute something on the way. Here, a possibility to proceed - for each field - would be to construct the corresponding field, the ring of polynomials over it, then define $p$ over this field, finally ask for the factorization. For instance:

Which is the code for the other two fields? (Of course, we can already decide...)