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Let f(x) be a nonzero polynomial in F[x]. Show that f(x) is a unit in F[x]...

Let f(x) be a nonzero polynomial in F[x]. Show that f(x) is a unit in F[x] if and only if f(x) is a nonzero constant polynomial, that is, f(x) =c where 0F is not equal to c where c is a subset of F. Hence deduce that F[x] is not a field.

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