The only expression that has a greatest common factor (GCF) of 3xy^2 with 42xy^4 is 3xy^2.
The greatest common factor (GCF) of two expressions is the largest expression that is a factor of both expressions.
To find the GCF of 3xy^2 and 42xy^4, we can factor each expression into its prime factorization:
3xy^2 = 3 * x * y * y
42xy^4 = 2 * 3 * 7 * x * y * x * y * y
The GCF of the two expressions is the product of the highest powers of each prime factor that appears in both expressions:
GCF(3xy^2, 42xy^4) = 3 * x * y * y = 3xy^2
Therefore, the only expression that has a greatest common factor (GCF) of 3xy^2 with 42xy^4 is 3xy^2.