Irreducible polynomials
Mention all the irreducible polynomials in Z 2 [x] of degree less than or equal to 4. Factor f(x)=(x^7)+1 bar as the product of irreducible polynomials in Z 2 [x].
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Compute the greatest common divisors d(x) of the following polynomials f(x),g(x) in the field F[x] and express d(x)=s(x)f(x)+t(x)g(x) for appropriate s(x), t(x) in F[x]: c. f(x)=(x^2)+1, g(x)=(x^2)-i+2, F=C (complex numbers) d. f(x)=(x^2)+2x+2, g
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