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Which of the following is a factor of x^2 - 9?

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Question: Which of the following is a factor of x^2 - 9?

Options:

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

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

Solution: 

x^2 - 9 is a difference of squares and can be factored as (x - 3)(x + 3).

Which of the following is a factor of x^2 - 9?

Practice Questions

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

Questions & Step-by-Step Solutions

Which of the following is a factor of x^2 - 9?
  • Step 1: Identify the expression you want to factor, which is x^2 - 9.
  • Step 2: Recognize that x^2 - 9 is a special type of expression called a 'difference of squares'.
  • Step 3: Recall the formula for factoring a difference of squares, which is a^2 - b^2 = (a - b)(a + b).
  • Step 4: In our case, a^2 is x^2 and b^2 is 9. So, a is x and b is 3 (since 3^2 = 9).
  • Step 5: Apply the difference of squares formula: Replace a with x and b with 3 in the formula.
  • Step 6: Write the factored form: (x - 3)(x + 3).
  • Step 7: Conclude that (x - 3)(x + 3) is the factorization of x^2 - 9.
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