Factor x^2 - 9.

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Multiple Choice

Factor x^2 - 9.

Explanation:
This is a difference-of-squares situation. x^2 - 9 can be seen as x^2 - 3^2. When you have a^2 - b^2, it factors as (a - b)(a + b). Here, a is x and b is 3, so it factors as (x - 3)(x + 3). Expanding to check: (x - 3)(x + 3) = x^2 + 3x - 3x - 9 = x^2 - 9, which matches perfectly. The constants must multiply to -9 and the x-term must cancel, which happens precisely with a 3 and a -3, yielding the factorization above.

This is a difference-of-squares situation. x^2 - 9 can be seen as x^2 - 3^2. When you have a^2 - b^2, it factors as (a - b)(a + b). Here, a is x and b is 3, so it factors as (x - 3)(x + 3).

Expanding to check: (x - 3)(x + 3) = x^2 + 3x - 3x - 9 = x^2 - 9, which matches perfectly.

The constants must multiply to -9 and the x-term must cancel, which happens precisely with a 3 and a -3, yielding the factorization above.

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