For a general polynomial #f(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+\cdots+a_{2}x^2+a_{1}x+a_{0}#, where #a_{n}!=0#, the degree is #n#, the terms are the terms you see for those #a#'s that are nonzero, and the coefficients are #a_{n},a_{n-1},a_{n-2},\ldots,a_{2},a_{1},a_{0}#. Whether you decide to include those #a#'s that are zero in your list of coefficients is, in a sense, dependent on what you are doing with the polynomial.
For example, if you are graphing it, then you don't need to worry about the #a#'s that are zero. On the other hand, if you are using synthetic division to confirm a root of the polynomial (or to divide it by #x-c#), then the #a#'s that are zero are important to include in your calculation.
