Final answer:
The greatest common factor (GCF) of the terms 97x⁸ and 87x⁵ is x⁵ because it is the largest exponent of x that divides both terms equally.
Step-by-step explanation:
The greatest common factor (GCF) of two terms is the largest factor that divides both numbers. To find the GCF of 97x⁸ and 87x⁵, we need to factor each term into its prime components and then determine the common factors.
Since 97 and 87 are both prime numbers, the only common numerical factor they have is 1. However, when we look at the variable parts, x⁸ and x⁵ share a common factor of x⁵, because x⁵ is the highest power of x that divides both x⁸ and x⁵ equally. Therefore, the GCF of 97x⁸ and 87x⁵ is x⁵.