What is the expression inside the parentheses after factoring out the GCF from 3x^2 - 12x - 36?

What is the expression inside the parentheses after factoring out the GCF from 3x^2 - 12x - 36?

• A. x^2 - 4x - 12
• B. x^2 + 4x - 12
• C. x^2 - 4x + 12
• D. x^2 - 2x - 6

Answer: (A)

Pull out the greatest common factor. Each term has a factor of 3, so factor 3 from the whole expression: 3(x^2 − 4x − 12). This inner expression is what sits inside the parentheses after factoring out the GCF. Checking by distributing back confirms 3(x^2 − 4x − 12) = 3x^2 − 12x − 36, so the inner expression is correct. Note that 3 is the largest common factor (6 wouldn’t work since 3x^2 isn’t divisible by 6). The inner trinomial can be factored further if needed, but for this question the expression inside is x^2 − 4x − 12.

Pull out the greatest common factor. Each term has a factor of 3, so factor 3 from the whole expression: 3(x^2 − 4x − 12). This inner expression is what sits inside the parentheses after factoring out the GCF. Checking by distributing back confirms 3(x^2 − 4x − 12) = 3x^2 − 12x − 36, so the inner expression is correct. Note that 3 is the largest common factor (6 wouldn’t work since 3x^2 isn’t divisible by 6). The inner trinomial can be factored further if needed, but for this question the expression inside is x^2 − 4x − 12.