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Assume $R$ is communtative. Let $x$ be an indeterminate, let $f(x)$ be a monic polynomial in $R[x]$ of degree $n \geq 1$, and use the bar notation to denote passage to the quotient ring $R[x]/(f(x))$.

So what do we mean by 'bar notation to denote passage to the quotient ring $R[x]/(f(x))$.'

Say in this context, what do the author mean if he/she use the term $\overline{a_{0}}$, $\ \overline{a_1x}$.

Any insight or help is appreciated.

EDIT:

I suppose I should just post the full question to avoid confusion.

Same setup as before,

Show that every element of $R[x]/(f(x))$ is of the form $\overline{p(x)}$ for some $p(x) \in R[x]$ of degree less than $n$.

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    $\bar{a}$ means the equivalence class of $a$ in the quotient. In other words, the image of $a$ under the canonical map $R[x] \to R[x]/(f(x))$. – 2017-01-31

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$\overline a$ is an element of $R[X]/(f(X))$, which one? The most reasonable one: $(f(x))+a$.