1. The problem is to factor the expression $9x^2 - 16$. 2. Recognize that this is a difference of squares, which follows the formula: $$a^2 - b^2 = (a - b)(a + b)$$ where $a$ and $b$ are expressions or numbers. 3. Identify $a$ and $b$ in $9x^2 - 16$: $$a = 3x, \quad b = 4$$ 4. Apply the difference of squares formula: $$9x^2 - 16 = (3x - 4)(3x + 4)$$ 5. Therefore, the factors of $9x^2 - 16$ are $(3x - 4)$ and $(3x + 4)$. 6. The other options given, such as $(9x - 4)$ or $(9x + 4)$, are incorrect because $9x$ is not the square root of $9x^2$; the square root is $3x$. Final answer: $(3x - 4)$ and $(3x + 4)$