Show that in a polynomial ring over a field K {\displaystyle {}K} , the following statement holds: if P , Q ∈ K [ X ] {\displaystyle {}P,Q\in K[X]} are not zero, then also
![{\displaystyle {}P,Q\in K[X]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f268286ca05e4e4b663e348b39b7a20a444f9e6e)
.