Exercise 1, § 8

Let $K$ be a commutative ring, $f(X)$ a monic polynomial in $K[X]$, $A$ the $K$-algebra $K[X]/(f)$ and $x$ the residue class of $X$ in $A$. For each $a \in K$ we have $f(a) = N_{A/K}(a - x)$.