Explanation

The first two terms in the algebraic expression are both divisible by x^{2}. Once we realize this, the question becomes much simpler: We only need concern ourselves with whether 6x + 9 is divisible by x^{2}.

Statement (1)

Since 4 < x^{2} < 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.

Statement (2)

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 x^{2}.

**The correct answer is C.**

Statement (1)

Since 4 < x

Statement (2)

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 x