Explanation of notation $\mathbb{F}_{s}[t]$

Question

I'm little bit confused:

In my textbook the set $\mathbb{F}_{s}[t]$ is defined as a set of all polynomials of variable $t$ and with coefficients of $\mathbb{F}$. A degree of those polynomials is maximum $s$.

Therefore it is logical if I have vector space $\mathbb{R}_{5}[x]$, I know the maximum degree of polynomials will be $x^5$.

Why does my workbook than says that the dimension of $\mathbb{R}_{5}[x]=6$?

Answer 1

Because you have the constant polynomial as well. A possible basis (the canonical one) is $(1,X,X^2,X^3,X^4,X^5)$.

Put differently, the degrees range from $0$ to $5$, so that's $5+1$.

Answer 2

Because you have one independent coefficient for each power of $x$, starting from $0$. $0,1,2,3,4,5$, or $6$ independent coefficients.