The number of polynomial in a polynomial ring

Question

If we define a poylnomail ring $R[x]$, I need to know the number of polynomial (in this ring) of a particular degree, $d$, please.Let $R=Z_P$, where $p$ is a prime number.

Answer 1

Such polynomials have the form $a_dx^x+a_{d-1}x^{d-1}+\ldots + a_1x+a_0$ where $a_d\ne 0$. From what we learn in combinatorics this gives us $(|R|-1)|R|^d$ poynomials.