Irreducible Field Functions
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Let F be a field and le p(x) E F[x]. If p(x) is not irreducible, then F[x]/{p(x)} is:
a) always a field
b) sometimes a field
c) never a field.
Give reasons for your assertion.
Please see attached.
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Solution Summary
The irreducible field functions are examined. The reasons for the assertions are provided.
Solution Preview
The answer is (c), never a field.
Proof:
Since p(x) is not irreducible, then it is reducible. We can find q(x) and r(x) with ...
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