Demonstrate Theorem 4.14 (attached below) by factoring p(x)= X^3 + 6 as a product of irreducible in Z7[X] in two ways. explain how your answer demonstrates the theorem.

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Theorem 4.14 Let F be a field. Every nonconstant polynomial f(x) in F[x] is a product of irreducible polynomials in F[x]. This factorization is unique in the following sense: If f(x) = p;(x)px) p.(x) f(x) = 9,(x)q;(x) • •q.(x) and Theorem 4.14 Let F be a field. Every nonconstant polynomial f(x) in F[x] is a product of irreducible polynomials in F[x]. This factorization is unique in the following sense: If f(x) = p;(x)px) p.(x) f(x) = 9,(x)q;(x) • •q.(x) and

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first we try to factor Px x 6 into irreducible ... View the full answer