Factor out the greatest common factor from 3x^2 - 12x - 36; which of the following is the correct factored form?

Factor out the greatest common factor from 3x^2 - 12x - 36; which of the following is the correct factored form?

• A. 3(x^2 - 4x - 12)
• B. 3(x^2 + 4x - 12)
• C. 2(x^2 - 4x - 18)
• D. x(3x - 12) - 36

Answer: (A)

Factoring out the greatest common factor means pulling out the largest factor that appears in every term. The terms 3x^2, -12x, and -36 share a factor of 3 (they don’t all share an x, since -36 has no x). Pulling out 3 gives 3(x^2 - 4x - 12). Distributing back confirms we get 3x^2 - 12x - 36, so this is the correct factored form. The other options either use the wrong factor, change the sign in the middle term, or don’t present a proper common-factor extraction.

Factoring out the greatest common factor means pulling out the largest factor that appears in every term. The terms 3x^2, -12x, and -36 share a factor of 3 (they don’t all share an x, since -36 has no x). Pulling out 3 gives 3(x^2 - 4x - 12). Distributing back confirms we get 3x^2 - 12x - 36, so this is the correct factored form. The other options either use the wrong factor, change the sign in the middle term, or don’t present a proper common-factor extraction.