Again, I know this one looks like it should be easy (easier, in fact, even than what I posted before). My brain is just completely fried on this subject right now for some reason...

Ahyperplanein is a hypersurface [which means its dimension (as a topological space in the Zariski topology on is ], which is defined by a single linear polynomial. That is, our hyperplane is , where is a linear, homogeneous (since we are in projective space) polynomial in ( an algebraically closed field) . The problem says to determine that is an affine variety.