Residue of x in polynomial ring $\mathbb{Z}\frac{x}{f}$

When we say that α is the residue of x in$\mathbb{Z}\frac{x}{f}$ , and $f={x}^{4}+{x}^{3}+{x}^{2}+x$ , wouldn't $\alpha$ just be x? Because if we divide with the remainder, we would get $x=0\text{}f+x$ ?

When we say that α is the residue of x in