The terms in a polynomial are multiples of powers of a particular variable separated by plus or minus signs.
So if p(x) is a polynomial called p in terms of a variable x, then p(x) is defined in terms of powers of x:
p(x)=anxn+an-1xn-1+...+a2x2+a1x+a0, where an are constants (positive or negative numbers, coefficients) and n is highest power (called the degree of the polynomial).
For example: q(x)=2x4-3x3-x2+5x+4 is a 4th degree polynomial in x (a4=2, a3=-3, a2=-1, a1=5, a0=4 are the coefficients).
A binomial is, for example, 3x-2 and has a degree of 1. Algebra deals with all degrees of polynomials.