Final answer:
To factor the quadratic equation x^2 + 9 over the complex numbers, we can express it as (x + 3i)(x - 3i), where i represents the square root of -1.
Step-by-step explanation:
When factoring a quadratic equation, we want to express it as a product of two binomials. In this case, we have the quadratic equation x^2 + 9. We can rewrite this as (x + 3i)(x - 3i), where i is the imaginary unit defined as the square root of -1. The complex numbers ±3i are the roots of the equation, meaning when we substitute these values for x, the equation becomes zero.