There is Polynomials by E.Barbeau contains all the basics, and has a lot of exercises too.
On a similar spirit is Polynomials by V.V. Prasolov.
I've found the treatment in both these books very nice, with lots of examples/applications and history of the results.
Oh, and in case you are interested in orthogonal polynomials, I believe the standard reference is Szegö's book.