Prime factor decomposition of a term like 10y²z³ gives some prime numbers and single variables, e.g., 2×5×y×y×z×z×z. In this example, 2 and 5 can be called prime factors, can't they? Can y and z be called prime factors also? If "no," is there one name suitable both for the prime numbers and single variables that we obtain after the prime factor decomposition? Thanks a lot in advance!
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$\begingroup$ I'm going to guess and say yes, x is a prime factor. Obviously, further on down the line, if x becomes an integer it might factor differently or further, but if that's the entire context, then x would be "prime". $\endgroup$– nickalhCommented Oct 13, 2021 at 20:29
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$\begingroup$ Some people would argue that irreducible polynomials behave much like primes (depending on the context). $\endgroup$– luluCommented Oct 13, 2021 at 20:32
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$\begingroup$ Some people would say irreducible polynomials are the generalisation of primes for polynomials of the variable being a generalised number. $\endgroup$– NijCommented Oct 13, 2021 at 22:20
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$\begingroup$ Thank you a bunch! Personally, I'd call them 'irreducible monomial factors' or maybe 'irreducible polynomials.' Not sure about the accepted term though. $\endgroup$– Error 403Commented Oct 14, 2021 at 6:04
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$\begingroup$ Welcome to MathSE. This tutorial explains how to typeset mathematics on this site. $\endgroup$– N. F. TaussigCommented Oct 14, 2021 at 7:56
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