A finite field F has q elements. If `alpha` is algebraic over F of degree n, then the field `F(alpha)` has `q^n` elements. To show the existence of a field with 8 elements, we can begin by considering the field `ZZ_2`.
What must be true about a polynomial f(x) over `ZZ_2` to allow us to construct a field of 8 elements using this idea:
A) The polynomial f(x) must be irreducible over `ZZ_2` and have a degree of 3.
B) The polynomial f(x) must have a root in `ZZ_2` and a degree of 8 ?