To determine the greatest common factor (GCF) of the terms [tex]\(24 s^3\)[/tex], [tex]\(12 s^4\)[/tex], and [tex]\(18 s\)[/tex], follow these steps:
1. Identify the coefficients of each term:
- For [tex]\(24 s^3\)[/tex], the coefficient is 24.
- For [tex]\(12 s^4\)[/tex], the coefficient is 12.
- For [tex]\(18 s\)[/tex], the coefficient is 18.
2. Find the GCF of the coefficients 24, 12, and 18:
- The factors of 24 are [tex]\(1, 2, 3, 4, 6, 8, 12, 24\)[/tex].
- The factors of 12 are [tex]\(1, 2, 3, 4, 6, 12\)[/tex].
- The factors of 18 are [tex]\(1, 2, 3, 6, 9, 18\)[/tex].
- The common factors of 24, 12, and 18 are [tex]\(1, 2, 3, 6\)[/tex]. Therefore, the GCF of 24, 12, and 18 is 6.
3. Identify the smallest power of [tex]\(s\)[/tex] common to all terms:
- For [tex]\(24 s^3\)[/tex], the power of [tex]\(s\)[/tex] is 3.
- For [tex]\(12 s^4\)[/tex], the power of [tex]\(s\)[/tex] is 4.
- For [tex]\(18 s\)[/tex], the power of [tex]\(s\)[/tex] is 1.
- The smallest power of [tex]\(s\)[/tex] common to all terms is [tex]\(s^1\)[/tex].
4. Combine the GCF of the coefficients with the smallest power of [tex]\(s\)[/tex]:
- The GCF of the coefficients is 6.
- The smallest power of [tex]\(s\)[/tex] is [tex]\(s^1\)[/tex] or simply [tex]\(s\)[/tex].
Thus, the greatest common factor of [tex]\(24 s^3\)[/tex], [tex]\(12 s^4\)[/tex], and [tex]\(18 s\)[/tex] is [tex]\(6 s\)[/tex].
So, the correct answer is:
[tex]\[
6s
\][/tex]
