which is a common monomial factor for the expression 45n² + 12mn? 12mn 3n 3n² 6mn²

Explanation:

Step1: Find the GCF of coefficients

Find the greatest common factor (GCF) of (45) and (12). Factors of (45): (1,3,5,9,15,45) Factors of (12): (1,2,3,4,6,12) GCF of (45) and (12) is (3).

Step2: Find the GCF of variables

For the variable part, in (n^{2}) (from (45n^{2})) and (mn) (from (12mn)), the common variable is (n) and the lowest power of (n) is (n^{1}=n).

Step3: Combine GCF of coefficients and variables

The common monomial factor is the product of the GCF of coefficients and the GCF of variables. So it is (3\times n = 3n). Check: (45n^{2}+12mn=3n(15n + 4m))

Answer:

(3n) (the second option)