3. Let F = Z5 and let f(x) = x + 2x + 1 F[r]. Let a be a root of f(x) in some extension of F. (a) Show that f(x) is irreducible in F[2]. (b) Find [F(a): F] and find a basis for F(a) over F. How many elements does F(a) have? (c) Write a + 2a + 3 in the form co + cia + c?a.

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3. Let F = Z5 and let f(x) = x + 2x + 1  F[r]. Let a be a root of f(x) in some extension of F. (a) Show that f(x) is irreducible in F[2]. (b) Find [F(a): F] and find a basis for F(a) over F. How many elements does F(a) have? (c) Write a + 2a + 3 in the form co + cia + c?a.

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Expert Answer to -  3. Let F = Z5 and let f(x) = x + 2x + 1  F[r]. Let a be a root of f(x) in some extension of F.

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Solution for -  3. Let F = Z5 and let f(x) = x + 2x + 1  F[r]. Let a be a root of f(x) in some extension of F.

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This an additional answer to -  3. Let F = Z5 and let f(x) = x + 2x + 1  F[r]. Let a be a root of f(x) in some extension of F.

(Solved): 3. Let F = Z5 and let f(x) = x + 2x + 1 F[r]. Let a be a root of f(x) in some extension of F. ...

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