She is not correct. The GCF for 2x^2 + 4xy + 8xy^4 is 2x The first term does not have a 'y' in it so you cannot have a 'y' in the GCF. The second and third terms both only have 1 'x', so you can only take out 1 'x', not 2. The highest constant that all three terms have in common is a 2.
