Let K {\displaystyle {}K} be a field and let K [ X ] {\displaystyle {}K[X]} be the polynomial ring over K {\displaystyle {}K} . Let a ∈ K {\displaystyle {}a\in K} . Prove that the evaluating function
satisfies the following properties (here let P , Q ∈ K [ X ] {\displaystyle {}P,Q\in K[X]} ).
![{\displaystyle {}K[X]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7861df9df3d7463835d927c4d0d4c27f5e2f8416)
![{\displaystyle \psi \colon K[X]\longrightarrow K,P\longmapsto P(a),}](https://wikimedia.org/api/rest_v1/media/math/render/svg/319779f46760396ed47e3abaf1c07de176917858)
![{\displaystyle {}P,Q\in K[X]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f268286ca05e4e4b663e348b39b7a20a444f9e6e)
