[nuancebydefault]

If you change the polynomial, you change the order of calculations and hence change behaviour. You might get overflows in case of integers or different precision in case of floats.

Nice to learn where the word originates from. Often the meaning of words change over time. E.g. today no horses need involved in bootstrapping.

[sevnin]

He said "I think" implying that he is not fully sure about the etymology. There is a history section on wikipedia for refactoring if you are interested.

[xigoi]

A polynomial is a mathematical object. There are no integer overflows or float imprecisions in mathematics.

[nuancebydefault]

You are right but in fact the maths are only a means to an end, a model that isn't exactly equal to the final real world implementation in analog or digital electronics.