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24-05-2023
Mathematics

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8. For each of the following polynomials, determine whether it is irreducible over the given ring and prove your answers.
(a) f(x) = 33 + x2 - 86 - 8; Z (b) g() = 4x + 2? +3; Z (c) h(x) = 162 - 2x2 +5; Q (d) px) = 2x + 1822 -- 15x+6; Q (e) g(x) = 1044 - x + x +7Q 9. Prove that Za[1/(x2 + + +1) is a field. How many elements does this field have?

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