Verify my polynomial proof

[Joe20]

I would like to have verification if the following attached proof is correct. If it is not correct, what can be done to make it correct? Thanks.

 

[I like Serena]

I would like to have verification if the following attached proof is correct. If it is not correct, what can be done to make it correct? Thanks.

Hi Alexis87,

It looks all correct to me.
For clarity I would just add a final sentence saying that therefore f(x+c) is reducible, which is a contradiction.