Determine whether the polynomial f(x) is irreducible over the indicated field. (a) f(x) = 4x^ 3...

Determine whether the polynomial f(x) is irreducible over the indicated field. (a) f(x) = 4x^ 3 + 10x^2 + 16x − 11 over Q (b) f(x) = 7x^ 4 − 9x^ 2 + 6 over Q (c) f(x) = x^3 − x + 1 over Q (d) f(x) = x ^4 + 2x ^2 + 2 over Q (e) f(x) = x^ 4 + 2x^ 2 + 2 over C (f) f(x) = x ^4 + 2x^ 2 + 2 over R (g) f(x) = x ^2 + 2x − 3 over Z-5 (h) f(x) = x ^3 − 2 over Z-7

Expert Solution

There are some irreducibility criterion which I have used,and these are available in any best book of abstract algebra..

Colby Messinger answered 2 years ago

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use the given zero to find the remaining zeros of each polynomial function 23. f(x)=x^3-4x^2+4x-16; zero;...

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