Marcia claims that the gcf for (2x2 + 4xy + 8xy4) is 8x2y4.
explain if she correct or not. if she is correct, justify her claim. if she is not correct, explain her error and state the correct gcf

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.