Giannisdagoatidn
Answered

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What is the greatest common factor of [tex]\(12a\)[/tex] and [tex]\(9a^2\)[/tex]?

A. 9
B. 36
C. [tex]\(3a\)[/tex]
D. [tex]\(12a^2\)[/tex]

Sagot :

GinnyAnsweridn
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].
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