Answer:
A. 5
Step-by-step explanation:
Since we are given the equation and our answer options are inputs, we can plug in our answer options and see which one does not yield a prime number and that would serve as a counterexample.
Solving:
[tex]\section*{}\subsection*{1. For \( x = 5 \)}\[x^2 + x + 5 = 5^2 + 5 + 5 = 25 + 5 + 5 = \boxed{35 \quad (\text{not prime})}\]\subsection*{2. For \( x = 11 \)}\[x^2 + x + 5 = 11^2 + 11 + 5 = 121 + 11 + 5 = 137 \quad (\text{prime})\]\subsection*{3. For \( x = 16 \)}\[x^2 + x + 5 = 16^2 + 16 + 5 = 256 + 16 + 5 = 277 \quad (\text{prime})\]\subsection*{4. For \( x = 21 \)}\[x^2 + x + 5 = 21^2 + 21 + 5 = 441 + 21 + 5 = 467 \quad (\text{prime})\][/tex]
Since 35 is not a prime number and is yielded from the equation when x = 5, this serves as our counter example, meaning the correct answer is A.