Polynomial ring/Field/Replacement/Structure/Exercise
Let be a field and let be the polynomial ring over . Let . Prove that the evaluating function
satisfies the following properties (here let ).
Let 
![{\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)
satisfies the following properties
(here let
![{\displaystyle {}P,Q\in K[X]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f268286ca05e4e4b663e348b39b7a20a444f9e6e)
