# 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 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 ...

#### Solution Summary

The irreducible field functions are examined. The reasons for the assertions are provided.

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