The real factors of x^2 + 4 are
A. (x^2 + 2)(x^2 - 2)
B. (x + 2)(x - 2)
C. does not exist
D. none of these

We are asked to find the real factors of the expression \(x^2 + 4\).

First, let's consider the expression \(x^2 + 4\). This is a quadratic expression, but it doesn't easily factor over the real numbers since it cannot be factored into terms with real coefficients. Specifically, the expression \(x^2 + 4\) is a sum of squares, which is not factorable into real binomials.

The expression \(x^2 + 4\) could be factored in the complex number system, but not in the real number system. In the complex domain, it factors as:
\[
x^2 + 4 = (x + 2i)(x - 2i)
\]
where \(i\) is the imaginary unit. However, since we are working with real numbers, this factorization is not valid.

Given the options:

A. \((x^2 + 2)(x^2 - 2)\) - This is not correct because expanding \((x^2 + 2)(x^2 - 2)\) gives \(x^4 - 4\), not \(x^2 + 4\).

B. \((x + 2)(x - 2)\) - This is not correct because expanding \((x + 2)(x - 2)\) gives \(x^2 - 4\), not \(x^2 + 4\).

C. Does not exist - This seems to be the correct answer because there are no real factors for \(x^2 + 4\).

D. None of these - This option is not correct because option C is correct.

Therefore, the correct answer is:

C. Does not exist