Mark each of the following true or false.
_ a. X — 2 is irreducible over ℚ.
_ b. 3x — 6 is irreducible over ℚ.
_ c. x2 — 3 is irreducible over ℚ.
_ d. x2 + 3 is irreducible over ℤ7.
_ e. If F is a field, the units of F[x] are precisely the nonzero elements of F.
_ f. If F is a field, the units of F(x) are precisely the nonzero elements of F.
_ g. A polynomial f(x) of degree n with coefficients in a field F can have at most n zeros in F.
_ h. A polynomial f(x) of degree n with coefficients in a field F can have at most n zeros in any given field E such that F ≤ E.
_ i. Every polynomial of degree 1 in F[x] has at least one zero in the field F.
_j. Each polynomial in F[x] can have at most a finite number of zeros in the field F.
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