To find the greatest common factor (GCF) of the terms [tex]\(12b\)[/tex] and [tex]\(8b^3\)[/tex], we will follow these steps:
1. Identify the coefficients and variable parts:
- The coefficients are 12 and 8.
- The variable parts are [tex]\(b\)[/tex] (for [tex]\(12b\)[/tex]) and [tex]\(b^3\)[/tex] (for [tex]\(8b^3\)[/tex]).
2. Find the GCF of the coefficients:
- The greatest common factor of 12 and 8 is 4. That is because 4 is the largest number that evenly divides both 12 and 8.
3. Determine the variable part of the GCF:
- Both terms have the variable [tex]\(b\)[/tex]. The term [tex]\(12b\)[/tex] has one [tex]\(b\)[/tex], and the term [tex]\(8b^3\)[/tex] has three [tex]\(b\)[/tex]s.
- The GCF for the variable part is the lowest power of [tex]\(b\)[/tex] common to both terms. In this case, it is [tex]\(b\)[/tex] (which is [tex]\(b^1\)[/tex]).
4. Combine the GCF of the coefficients and the variable part:
- The GCF of the coefficients is 4, and the GCF of the variable part is [tex]\(b\)[/tex].
- Therefore, the GCF of [tex]\(12b\)[/tex] and [tex]\(8b^3\)[/tex] is [tex]\(4b\)[/tex].
Thus, the greatest common factor of [tex]\(12b\)[/tex] and [tex]\(8b^3\)[/tex] is [tex]\(\boxed{4b}\)[/tex].
