) = x^2 + 3x + 1 is irreducible in Z7[x]. (b) g(x) = x^3 + 3x^2 + x + 1 is irreducible in Z7[x] can you show all the step please

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter3: Polynomial And Rational Functions
Section3.5: Complex Zeros And The Fundamental Theorem Of Algebra
Problem 3E: A polynomial of degree n I has exactly ____________________zero if a zero of multiplicity m is...
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Prove that:
(a) f (x) = x^2 + 3x + 1 is irreducible in Z7[x].
(b) g(x) = x^3 + 3x^2 + x + 1 is irreducible in Z7[x]

can you show all the step please

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