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  • $\begingroup$ It doesn't make sense to say that $n$ depends on neither $c$ nor $b$. If you were to word it as "Does there exist an $n$ such that for all $b,c$, there exist a polynomial of degree $n$ such that ..." Also, your first condition can almost be simplified to "the absolute value is strictly increasing". $\endgroup$ Commented Dec 17, 2020 at 1:43
  • $\begingroup$ @Acccumulation Noted and changed accordingly. $\endgroup$ Commented Dec 17, 2020 at 2:22