Final answer:
To find the greatest common factor of 35b^2, 15b^3, and 5b, determine the highest power of each factor present in all terms. The GCF is the product of these common factors, which is 5b. Therefore, the correct answer is (a) 5b.
Step-by-step explanation:
To find the greatest common factor (GCF) of the given expressions, we should identify the highest power of each prime factor that is present in every term. Let's factor each term individually:
- 35b^2 = 5 × 7 × b × b
- 15b^3 = 3 × 5 × b × b × b
- 5b = 5 × b
Now, we determine the common factors in each term:
- The smallest power of b that appears in all three expressions is b to the first power (b^1).
- The common numerical factor that appears in all terms is 5.
Therefore, the GCF is the product of these common factors, which is 5b. So the correct answer is (a) 5b.