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

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

Options:

Correct Answer: Both x - 3 and x + 3

Solution:

The polynomial x^2 - 9 can be factored as (x - 3)(x + 3).

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

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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