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Which of the following is the correct factorization of x^2 - 9?

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Question: Which of the following is the correct factorization of x^2 - 9?

Options:

  1. (x - 3)(x + 3)
  2. (x - 3)(x - 3)
  3. (x + 3)(x + 3)
  4. (x - 9)(x + 1)

Correct Answer: (x - 3)(x + 3)

Solution: 

Step 1: Recognize it as a difference of squares: a^2 - b^2 = (a - b)(a + b). Step 2: Here, a = x, b = 3. So, (x - 3)(x + 3).

Which of the following is the correct factorization of x^2 - 9?

Practice Questions

Q1
Which of the following is the correct factorization of x^2 - 9?
  1. (x - 3)(x + 3)
  2. (x - 3)(x - 3)
  3. (x + 3)(x + 3)
  4. (x - 9)(x + 1)

Questions & Step-by-Step Solutions

Which of the following is the correct factorization of x^2 - 9?
Correct Answer: (x - 3)(x + 3)
  • Step 1: Identify the expression x^2 - 9. Notice that it can be written as a difference of squares because it is in the form a^2 - b^2.
  • Step 2: Recognize that a = x (since x^2 is x squared) and b = 3 (since 9 is 3 squared).
  • Step 3: Apply the difference of squares formula, which states that a^2 - b^2 = (a - b)(a + b).
  • Step 4: Substitute a and b into the formula: (x - 3)(x + 3).
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