Final answer:
The greatest common factor (GCF) of 4x²y⁶ and 18xy⁵ is 2xy⁵, as it is the product of the highest common factors of their numerical coefficients and variables with the lowest exponents.
Step-by-step explanation:
The question involves finding the greatest common factor (GCF) of two algebraic expressions: 4x²y⁶ and 18xy⁵. To find the GCF, we need to identify the smallest exponent for each base that appears in both terms and use the lowest coefficient that is a factor of both numerical coefficients.
Starting with the numerical coefficients, the GCF of 4 and 18 is 2 since it is the largest integer that divides into both 4 and 18. For the variable x, since we have x² in the first term and x in the second, the lowest exponent of x is 1. For the variable y, we have y⁶ in the first term and y⁵ in the second term; therefore, the GCF contains y with the lowest exponent, which is 5.
The GCF of 4x²y⁶ and 18xy⁵ is therefore 2xy⁵, which corresponds to option (a) 2xy.