Get detailed and reliable answers to your questions on IDNLearn.com. Ask your questions and get detailed, reliable answers from our community of knowledgeable experts.
Sagot :
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].
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].
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. For trustworthy and accurate answers, visit IDNLearn.com. Thanks for stopping by, and see you next time for more solutions.