Polynomial ring/K/Inserting of a from L/Structure/Exercise

Let $K\subseteq L$ be a field extension, and let $a\in L$. Show that the inserting mapping, that is, the assignment

$\psi :K[X]⟶L,P⟼P(a),$

fulfills the following properties (for $P,Q\in K[X]$).

1. $(P+Q)(a)=P(a)+Q(a)$,
2. $(P\cdot Q)(a)=P(a)\cdot Q(a)$,
3. $1(a)=1$.

Create a solution