1670s (n.), in algebra, "an expression consisting of many terms;" 1704 (adj.), "containing many names or terms;" irregularly formed from poly- + stem of binomial. By 1885 as "a technical name consisting of more than two terms."
word-forming element meaning "many, much, multi-, one or more," from Greek polys "much" (plural polloi), from PIE root *pele- (1) "to fill," with derivatives referring to multitudinousness or abundance. Equivalent to Latin multi-, it is properly used in compounds only with words of Greek origin. In chemical names, usually indicating a compound with a large number of atoms or molecules of the same kind (such as polymer).
1550s, "an algebraic expression consisting of two terms," from Late Latin binomius "having two personal names," a hybrid from bi- "two" (see bi-) + nomius, from nomen (from PIE root *no-men- "name"). In zoology and botany, "a name consisting of two terms, generic and specific."
<a href="https://www.etymonline.com/word/polynomial">Etymology of polynomial by etymonline</a>
Harper, D. (n.d.). Etymology of polynomial. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/polynomial