Final answer:
Option (a) x² + 6x + 9 is the only perfect-square quadratic expression among the options given, as it can be factored into (x + 3)^2, fulfilling the perfect square conditions.
Step-by-step explanation:
The question asks us to identify which of the given options is a perfect-square quadratic expression. A perfect-square quadratic expression is one that can be factored into the square of a binomial. Hence, we are looking for an expression of the form (ax + b)^2, which when expanded becomes a^2x^2 + 2abx + b^2. We can assert that option (a) x² + 6x + 9 is the correct choice because it can be factored into (x + 3)^2, making it a perfect square. The other options cannot be factored into perfect squares as their coefficients do not satisfy the necessary condition a^2x^2 + 2abx + b^2.
To further elaborate, in the expression from option (a), a=1, b=3, and we can verify that the middle term is twice the product of a and b (i.e., 2*1*3 = 6) and the constant term is the square of b (i.e., 3^2 = 9).
Therefore, the mention correct option in the final answer is (a) x² + 6x + 9, and it is the only option that forms a perfect square when factored. You should choose only one option for a question about perfect squares, and in this case, (a) is the correct one.