To find the greatest common factor (GCF) of the given algebraic terms [tex]\(24s^3\)[/tex], [tex]\(12s^4\)[/tex], and [tex]\(18s\)[/tex], follow these steps:
1. Identify the numerical coefficients:
- The coefficient of [tex]\(24s^3\)[/tex] is 24.
- The coefficient of [tex]\(12s^4\)[/tex] is 12.
- The coefficient of [tex]\(18s\)[/tex] is 18.
2. Find the GCF of the numerical coefficients:
- The GCF of 24, 12, and 18 can be determined by finding the highest number that divides all three coefficients without leaving a remainder.
- 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 these numbers are [tex]\(1, 2, 3, 6\)[/tex].
- The greatest common factor of 24, 12, and 18 is [tex]\(6\)[/tex].
3. Identify the variable part [tex]\(s\)[/tex]:
- For [tex]\(s\)[/tex], we consider the lowest power of [tex]\(s\)[/tex] present in all terms.
- In [tex]\(24s^3\)[/tex], the exponent of [tex]\(s\)[/tex] is 3.
- In [tex]\(12s^4\)[/tex], the exponent of [tex]\(s\)[/tex] is 4.
- In [tex]\(18s\)[/tex], the exponent of [tex]\(s\)[/tex] is 1.
- The lowest exponent among these is [tex]\(1\)[/tex].
4. Combine the numerical GCF and the variable part:
- The GCF of the coefficients is 6.
- The lowest power of [tex]\(s\)[/tex] is [tex]\(s^1\)[/tex] or simply [tex]\(s\)[/tex].
Therefore, the greatest common factor of [tex]\(24s^3\)[/tex], [tex]\(12s^4\)[/tex], and [tex]\(18s\)[/tex] is [tex]\(6s\)[/tex].
So, the correct answer to the question is:
[tex]\[ 6s \][/tex]
