Let K {\displaystyle {}K} be a field, let K [ X ] {\displaystyle {}K[X]} be the polynomial ring over K {\displaystyle {}K} and a ∈ K {\displaystyle {}a\in K} . Then the evaluation mapping
is K {\displaystyle {}K} -linear. Moreover, we have
see exercise.
![{\displaystyle {}K[X]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7861df9df3d7463835d927c4d0d4c27f5e2f8416)
![{\displaystyle K[X]\longrightarrow K,P\longmapsto P(a),}](https://wikimedia.org/api/rest_v1/media/math/render/svg/969d7fce437cbcd2340b16f58e231736b4a3e991)
