Prove Corollary 1 and 2 of Theorem 16.2. Corollary 1 of Theorem 16.2 states: Let F be a field, a ∈ F, and f(x) ∈ F[x]. Then f(a) is the remainder in the division of f(x) by x – a. Corollary 2 of Theorem 16.2 states: Let F be a field, a ∈ F, and f(x) ∈ F[x]. Then a is a zero of f(x) if and only if  x – a is a factor of f(x). Contemporary Abstract Algebra

Q: of F(a) tha 34. Show that {a + b(2) + c(/2)² | a, b, c e Q} is a subfield of R by using the ideas of…

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Q: (9.1) Show that 3 ∈ Z15 is a zero divisor. (9.2) Prove that in any ring R, if a ∈ R is a zero…

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Q: 31. Let F be a field and f(x), g(x) e F[x]. Show that f(x) divides g(x) if and only if g(x)E (f(x)).…

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Q: 9. Use the field norm to show: a) 1+/2 is a unit in Z [/2] b) -1+v-3 is a unit in Z [1+-3 ]

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Q: in extension of a fie elements in K which ver F from a subfie

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