In ring theory, a polynomial over a rings, say ## R[x] ## is presented as an abstract object of the form:(adsbygoogle = window.adsbygoogle || []).push({});

## p(x) = a_{n}x^{n} + ...+ a_{1}x + a_{0} ## where the coefficients ## a_{n}...a_{0} ## are from a ring R with unity and ##x## is a formal symbol.

So what is the significance of ## p(x+1) ## ? In a high school algebra, one would simply interpret this as ##p(x)## with every instance of the variable ##x## replaced by ##x+1##. But in this notation, what does ## x + 1 ## even mean? It is itself a one-degree polynomial of ## R[x]## but then what does the notation ##p(x+1)## refer to?

BiP

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# Polynomials over a ring evaluated at a value?

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