Factor 3x^2 + 9x + 6.

Factor 3x^2 + 9x + 6.

• A. (3x + 9)(x + 2)
• B. 3(x^2 + 3x + 2)
• C. 3x(x + 3) + 6
• D. (3x + 6)(x + 1)

Answer: (B)

Pull out the greatest common factor. All three terms share a 3, so you can factor it out: 3(x^2 + 3x + 2). This shows the expression in a simpler, factored-with-respect-to-a-factor form. The inner quadratic can further be broken down as x^2 + 3x + 2 = (x + 1)(x + 2), giving the fully factored form 3(x + 1)(x + 2). The other forms don’t reflect this factoring step or, in some cases, change the middle and constant terms, so they aren’t the clean representation of the factoring process.

Pull out the greatest common factor. All three terms share a 3, so you can factor it out: 3(x^2 + 3x + 2). This shows the expression in a simpler, factored-with-respect-to-a-factor form. The inner quadratic can further be broken down as x^2 + 3x + 2 = (x + 1)(x + 2), giving the fully factored form 3(x + 1)(x + 2). The other forms don’t reflect this factoring step or, in some cases, change the middle and constant terms, so they aren’t the clean representation of the factoring process.