Final answer:
The GCF of the expression 2πrh + πr^2, which represents the surface area of a soup can without a lid, is πr, corresponding to option d).
Step-by-step explanation:
The student has asked what the Greatest Common Factor (GCF) is for the expression modeling the surface area of a soup can without a lid, which is given as 2πrh + πr^2. The GCF is the largest expression that divides into each term of the given expression without leaving a remainder.
We can find the GCF by identifying the common factors in each term. Both terms have π and r as factors, but only the first term has the factor of 2. Thus, the GCF does not include the number 2. The second term limits the power of r to 1, because that's the highest power of r that appears in all terms of the expression. Therefore, the GCF is πr, which corresponds to option d).