What is the greatest common factor that can be factored from 3x^2 - 12x - 36?

What is the greatest common factor that can be factored from 3x^2 - 12x - 36?

• A. 3
• B. 1
• C. 9
• D. 6

Answer: (A)

The idea here is to pull out the largest common factor from every term. Look at the coefficients: 3, -12, and -36. The greatest common divisor of these numbers is 3, and there’s no x factor that all terms share (the last term has no x at all). So you can factor out a 3: 3x^2 - 12x - 36 = 3(x^2 - 4x - 12). This is the greatest factor you can pull out. (If you want, you can factor the inside further: x^2 - 4x - 12 = (x - 6)(x + 2).) The other choices don’t work because 6 or 9 don’t divide all the coefficients, and 1 is smaller than the true greatest common factor.

The idea here is to pull out the largest common factor from every term. Look at the coefficients: 3, -12, and -36. The greatest common divisor of these numbers is 3, and there’s no x factor that all terms share (the last term has no x at all). So you can factor out a 3:

3x^2 - 12x - 36 = 3(x^2 - 4x - 12).

This is the greatest factor you can pull out. (If you want, you can factor the inside further: x^2 - 4x - 12 = (x - 6)(x + 2).) The other choices don’t work because 6 or 9 don’t divide all the coefficients, and 1 is smaller than the true greatest common factor.