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The expression given is \( x^2 + 4 \).

This is a sum of squares, which does **not** factor into real numbers. The sum of squares formula, unlike the difference of squares, does not provide an easy real number factorization. However, if we consider complex numbers, we can express it as:

\[
x^2 + 4 = (x + 2i)(x - 2i)
\]

Here, \( i \) is the imaginary unit where \( i^2 = -1 \).

Would you like a more detailed explanation on this or have any specific questions? Here are some follow-up questions you may consider:

1. What is the difference between factoring sum of squares and difference of squares?
2. How do you factor a quadratic expression that is not a sum or difference of squares?
3. What is the significance of the imaginary unit \( i \) in mathematics?
4. How do you solve quadratic equations involving complex numbers?
5. What methods can be used to determine whether an expression is factorable in real numbers?

**Tip:** When factoring expressions involving squares, always check whether you're dealing with a sum of squares or a difference of squares—only the latter is factorable with real numbers!

Completely factor the expression x^2 + 4.

Learn how to factor the expression x^2 + 4 by using complex numbers. This problem involves algebraic techniques and understanding the imaginary unit 'i', where i^2 = -1. Suitable for high school students in Grades 10-12.

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