Types of polynomial functions. Quadratic, cubic, quartic, quintic, ...,?

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I would very much like to have a complete list of the types of polynomial functions. I know that theres:

Quadratic : (AX^2 + BX + C)
Cubic : (AX^3 + BX^2 + CX + D)
Quartic : (AX^4 + BX^3 + CX^2 + DX + E)
Quintic : (AX^5 + BX^4 + CX^3 + DX^2 + EX + F)

What are the names of polynomial functions to the further powers? Sexstic? Septic? Octic? I'm not sure, so if someone could enlighten me, then that would be great. Please provide a list that goes at least to the seventh power, but it would be nice if you could go further. Thanks.

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2 Answers

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While they do start getting awkward quickly, the next few ordinals are fairly well-defined, largely because of their occasional usage in solving cubic and quartic equations and in defining algebraic curves and surfaces: the Sextic, the Septic, and the Octic. Beyond that, they just don't show up often enough to be worth explicitly naming.

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I think after quintic it becomes cumbersome to name them (since the prefixes become increasingly more complex). Thus, I feel like "degree seven" or "seventh degree" polynomial is more appropriate. If you are really interested in the prefixes look here under "ordinal".

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