To find the greatest common factor (GCF) of the terms [tex]\(12a\)[/tex] and [tex]\(9a^2\)[/tex], we need to follow these steps:
1. Identify the coefficients: The coefficients in the given terms are 12 and 9.
2. Find the GCF of the coefficients:
- The factors of 12 are: 1, 2, 3, 4, 6, 12.
- The factors of 9 are: 1, 3, 9.
- The common factors of 12 and 9 are: 1, 3.
- The greatest common factor (GCF) of 12 and 9 is the largest common factor, which is 3.
3. Identify the variable part:
- The first term is [tex]\(12a\)[/tex], which has the variable [tex]\(a\)[/tex].
- The second term is [tex]\(9a^2\)[/tex], which has the variable [tex]\(a^2\)[/tex].
4. Determine the common variable part:
- The lowest power of [tex]\(a\)[/tex] common to both terms is [tex]\(a\)[/tex], since [tex]\(a\)[/tex] is common between the two terms and it is the lowest power present in both.
5. Combine the GCF of the coefficients with the common variable part:
- The GCF of the coefficients is 3.
- The common variable factor is [tex]\(a\)[/tex].
By combining these, the greatest common factor (GCF) of [tex]\(12a\)[/tex] and [tex]\(9a^2\)[/tex] is [tex]\(3a\)[/tex].
Thus, the correct answer is: [tex]\(3a\)[/tex].
