Factor the quadratic 3x^2 - 12x + 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

Factor the quadratic 3x^2 - 12x + 9.

Explanation:
Factoring a quadratic starts by pulling out any common factor, then breaking the remaining quadratic into two binomials. For 3x^2 - 12x + 9, first factor out the 3 to get 3(x^2 - 4x + 3). Now factor the inside: look for two numbers that multiply to 3 and add to -4. Those numbers are -1 and -3, so x^2 - 4x + 3 = (x - 1)(x - 3). Therefore the whole expression factors as 3(x - 1)(x - 3). If you expand different forms, you’d get a different middle term or constant, so this is the correct factorization.

Factoring a quadratic starts by pulling out any common factor, then breaking the remaining quadratic into two binomials. For 3x^2 - 12x + 9, first factor out the 3 to get 3(x^2 - 4x + 3). Now factor the inside: look for two numbers that multiply to 3 and add to -4. Those numbers are -1 and -3, so x^2 - 4x + 3 = (x - 1)(x - 3). Therefore the whole expression factors as 3(x - 1)(x - 3). If you expand different forms, you’d get a different middle term or constant, so this is the correct factorization.

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