Sure! Let's find the greatest common factor (GCF) of the two terms [tex]\(12a\)[/tex] and [tex]\(9a^2\)[/tex].
1. Identify the coefficients and the variables:
- For the term [tex]\(12a\)[/tex], the coefficient is 12, and the variable is [tex]\(a\)[/tex] raised to the power of 1.
- For the term [tex]\(9a^2\)[/tex], the coefficient is 9, and the variable is [tex]\(a\)[/tex] raised to the power of 2.
2. Find the GCF of the coefficients:
- The coefficients here are 12 and 9.
- The greatest common divisor (GCD) of 12 and 9 is 3.
3. Determine the common variable part with the lowest power:
- Both terms have the variable [tex]\(a\)[/tex], with the powers [tex]\(a^1\)[/tex] and [tex]\(a^2\)[/tex].
- The lowest power of [tex]\(a\)[/tex] common to both terms is [tex]\(a^1\)[/tex].
4. Combine the GCF of the coefficients with the common variable part:
- The GCF of the coefficients is 3.
- The common variable part is [tex]\(a^1\)[/tex], which is simply [tex]\(a\)[/tex].
Therefore, the greatest common factor of the terms [tex]\(12a\)[/tex] and [tex]\(9a^2\)[/tex] is:
[tex]\[
3a
\][/tex]
So the correct answer is [tex]\(3a\)[/tex].
