Factor the polynomial x^2 - 9.

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Question: Factor the polynomial x^2 - 9.

Options:

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

Solution:

The expression x^2 - 9 is a difference of squares, which factors to (x - 3)(x + 3).

Factor the polynomial x^2 - 9.

Factor the polynomial x^2 - 9.

Step 1: Identify the polynomial you want to factor, 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 formula for factoring a difference of squares: a^2 - b^2 = (a - b)(a + b).
Step 5: Substitute a and b into the formula: (x - 3)(x + 3).
Step 6: Write the final factored form: x^2 - 9 = (x - 3)(x + 3).

Difference of Squares – A mathematical identity that states a^2 - b^2 = (a - b)(a + b), used to factor polynomials.