The problem asks to factor the polynomial $x^3 + 27$.

This is a sum of cubes, as $x^3 + 27 = x^3 + 3^3$. The formula for factoring a sum of cubes is:

$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$

In this case, $a = x$ and $b = 3$. Applying the formula:

$x^3 + 27 = (x + 3)(x^2 - 3x + 9)$

So, the correct factorization is $(x + 3)(x^2 - 3x + 9)$.

From the provided options, the first one matches this factorization: $(x + 3)(x^2 - 3x + 9)$

Thus, the correct answer is the first option.

Would you like any further details or have any questions?

Here are 5 related questions you might explore:

1. How do you factor a difference of cubes?
2. What are the general formulas for factoring special polynomials?
3. How would you solve the equation $x^3 + 27 = 0$?
4. What is the significance of the quadratic term in sum of cubes factoring?
5. How would you expand $(x + 3)(x^2 - 3x + 9)$ back to the original polynomial?

Tip: Always look for special patterns like sum or difference of cubes to simplify complex expressions easily!