Factor 6x^2 + 9x.

Factor 6x^2 + 9x.

• A. 6x^2 + 9x
• B. 3x(2x + 3)
• C. 6x(x + 1.5)
• D. (3x^2 + 9x)

Answer: (B)

Pull out the greatest common factor. Both terms share 3x, so factor that out: 6x^2 + 9x = 3x(2x) + 3x(3) = 3x(2x + 3). This shows the common factor and what remains inside the parentheses, giving the simplest factorization with integer coefficients. The decimal option is algebraically valid but less preferred, since it uses a non-integer inside the parentheses (6x(x + 3/2)). The form 3x^2 + 9x would factor to 3x(x + 3), which is a different expression and does not equal the original.

Pull out the greatest common factor. Both terms share 3x, so factor that out: 6x^2 + 9x = 3x(2x) + 3x(3) = 3x(2x + 3). This shows the common factor and what remains inside the parentheses, giving the simplest factorization with integer coefficients. The decimal option is algebraically valid but less preferred, since it uses a non-integer inside the parentheses (6x(x + 3/2)). The form 3x^2 + 9x would factor to 3x(x + 3), which is a different expression and does not equal the original.