Irreducibility is what makes one root generate the whole splitting field

1. A.Let f(X) ∈ 𝔽_p[X] and $\alpha$ be a root of f in 𝔽̄_p. Then 𝔽$_p(\alpha)$ is the splitting field of f in 𝔽̄_p.
2. B.Let f, g ∈ 𝔽_p[X] be irreducible polynomials of same degree and $\alpha$ be a root of f in 𝔽̄_p. Then 𝔽$_p(\alpha)$ is the splitting field of g in 𝔽̄_p.✓ Correct
3. C.𝔽_p[X] has infinitely many irreducible polynomials.✓ Correct
4. D.The set {a + b | a, b ∈ 𝔽_p} is contained in {$a^{2} + b^{2}$ | a, b ∈ 𝔽_p}.✓ Correct

The trap it tests

A theorem applied without checking one of its preconditions.