When you foil it out you should get: 2x^5-2x^3-12x. When you factor it out completely you get: 2x(x^2-3)(x^2+2)
There is no solutions, I think you got the signs mixed up.
A polynomial is a collection of terms that are separated by a plus or a minus sign. There a few types of polynomials.
Monomials have one term.
Binomials have two terms.
Trinomials have three terms.
All of these are classified as a polynomial.
Once you go over 3 terms, it's simply called a polynomial.