The first two terms in the algebraic expression are both divisible by x2. Once we realize this, the question becomes much simpler: We only need concern ourselves with whether 6x + 9 is divisible by x2.
Since 4 < x2 < 30 and x is prime, we know that x is a prime number greater than 2 and less than or equal to 5. This means x is either 3 or 5. Testing these values in 6x + 9, we find that the expression is divisible for x = 3 but not x = 5. This statement is insufficient.
The answer must be B, C, or E.
Factoring the quadratic equation gives us (x − 3)(x − 7) = 0, and x = 3 or 7. Both are prime, so both are possible values for x. Testing these values in 6x + 9, we find that the expression is divisible for x = 3 but not x = 7. This statement is not sufficient.
The correct answer is C or E.
Statement (1 & 2)
The only solution for the two statements taken together is x = 3, and the expression in the question stem is divisible by x2.
The correct answer is C.