Question

Marcia claims that the GCF for (2x2 + 4xy + 8xy4) is 8x2y4.

Answer 1

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.