Show that the following polynomials are irreducible over Q. (a) (8 points) f(1) = 5.rº –...

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Question

Show that the following polynomials are irreducible over Q. (a) (8 points) f(1) = 5.rº – 1826 + 30x4 – 6r2 + 12x + 60 (b) (12

Answer 1

Answer #1

eisenstein criterion for irreducibility

f(x) = ax + an-1 + ... + a, EZ[x]. If there is a prime p such that płapla-p...,pla, and p2 + a,, then f(x) is irreducible ov

gca) = x-on aton? 42 +3 Now we are going to be the fact that fox) is imeducible over g iff fexta is irreducible over a g for

Answer 2

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