harmonic functions

I'm sure these have easy answers ... I mean just by using
definitions & basic facts ... but I'm having troubles
with them. So that you know, they are homework problems.
My brain is in stupid mode. Can anybody help please?

eg.,
how can we find all the harmonic (real) poly. u(x,y)?

[I was thinking we know what a poly looks like & we know
harmonic funcitons must satisfy Laplace's eqn ... so, see
what poly satisfy Laplace's eqn & that's my answer]


eg.,
Or another one is given a twice diff. funciton h:R->R^2 &
a harmonic function u:R^2->R such that u(x,y)=h(x)h(y),
what is the general expression for h?

There are many other questions similar to this too (they
just change the 'such that .. = ' condition).

[ I was thinking to do the same sort of hting as above
since we know it makes sense to take 2nd deriv's of h]


... yes? no? Help please :(
.