Factor completely: x^2 - 9.

Factor completely: x^2 - 9.

• A. (x - 9)(x + 1)
• B. (x - 3)(x - 3)
• C. (x - 3)(x + 3)
• D. (x + 9)(x - 1)

Answer: (C)

The expression x^2 - 9 is a difference of squares. Each term is a perfect square: x^2 and 3^2. When you have a^2 - b^2, it factors as (a - b)(a + b). Here a is x and b is 3, so it factors to (x - 3)(x + 3). Expanding confirms the result: (x - 3)(x + 3) = x^2 + 3x - 3x - 9 = x^2 - 9. Other factorizations would produce a nonzero x-term or a different constant, so they don’t match x^2 - 9.

The expression x^2 - 9 is a difference of squares. Each term is a perfect square: x^2 and 3^2. When you have a^2 - b^2, it factors as (a - b)(a + b). Here a is x and b is 3, so it factors to (x - 3)(x + 3). Expanding confirms the result: (x - 3)(x + 3) = x^2 + 3x - 3x - 9 = x^2 - 9. Other factorizations would produce a nonzero x-term or a different constant, so they don’t match x^2 - 9.