It's kind of crazy to me that two different polynomials can induce the same function. That seems so contrary to everything I have learned before and it's a weird idea to think about. It's also kinda of cool though that you can just substitute all possible values of x in that ring, see that for each polynomial they map to the same elements, and then you can see that you really have the same function.
It's difficult to think of x has have two different roles. The hardest part of this is that it can change whether a statement is true or false based on what the meaning of x is in that particular context. Tricky!
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