1 Verify whether two polynomials with rational coefficients X 4 X 3 X 2 X 1 and X 3 X 2 X 1 are relatively prime or not 2 Prove that polynomial X 3 X X 3 is irreducible in Z5 X and that it is reducible in Z 3 X Factor it into a product of irreducible polynomials in the latter case Show the work

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Question: 1. Verify whether two polynomials with rational coefficients X 4 + X 3 + X 2 + X + 1 and X 3 + X

1. Verify whether two polynomials with rational coefficients X⁴ + X³ + X² + X + 1 and X³ + X² + X + 1 are relatively prime or not.

2. Prove that polynomial X³+ X² + X + 3 is irreducible in Z5 [X] and that it is reducible in Z³[X]. Factor it into a product of irreducible polynomials in the latter case. Show the work.

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