quarrel vs polemize

quarrel is a noun but polemize is not a noun.

Word	Noun	Adjective	Verb	Adverb
quarrel	Yes	No	Yes	No
polemize	No	No	Yes	No

As verbs, polemize is a hyponym of quarrel; that is, polemize is a word with a more specific, narrower meaning than quarrel:

Other hyponyms of quarrel include brawl, wrangle, spat, polemicise, polemicize, polemise, fall out.

quarrel (noun)	polemize (noun)
an arrow that is shot from a crossbow; has a head with four edges
an angry dispute

quarrel (verb)	polemize (verb)
have a disagreement over something	engage in a controversy