Factorize the polynomial x^2 - 9.

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

Factorize the polynomial x^2 - 9.

Explanation:
Recognize a difference of squares: a^2 - b^2 = (a - b)(a + b). Here a is x and b is 3, since 9 = 3^2. So x^2 - 9 factors to (x - 3)(x + 3). Expanding confirms it: (x - 3)(x + 3) = x^2 - 9. Other forms would produce an x term or a different constant, so they don’t match x^2 - 9.

Recognize a difference of squares: a^2 - b^2 = (a - b)(a + b). Here a is x and b is 3, since 9 = 3^2. So x^2 - 9 factors to (x - 3)(x + 3). Expanding confirms it: (x - 3)(x + 3) = x^2 - 9. Other forms would produce an x term or a different constant, so they don’t match x^2 - 9.

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