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

Practice Questions

Q1
Which of the following is a factor of the polynomial x^2 - 9?
  1. x - 3
  2. x + 3
  3. Both x - 3 and x + 3
  4. None of the above

Questions & Step-by-Step Solutions

Which of the following is a factor of the polynomial x^2 - 9?
  • Step 1: Identify the polynomial we are working with, which is x^2 - 9.
  • Step 2: Recognize that x^2 - 9 is a difference of squares. A difference of squares has the form a^2 - b^2.
  • Step 3: In this case, a^2 is x^2 (where a = x) and b^2 is 9 (where b = 3).
  • Step 4: Use the difference of squares formula, which states that a^2 - b^2 = (a - b)(a + b).
  • Step 5: Substitute a and b into the formula: (x - 3)(x + 3).
  • Step 6: Conclude that the factors of the polynomial x^2 - 9 are (x - 3) and (x + 3).
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