polemize vs quarrel

polemize is not a noun while quarrel is a noun.

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

As verbs, quarrel is a hypernym of polemize; that is, quarrel is a word with a broader meaning than polemize:

Other hypernyms of polemize include altercate, argufy, dispute, scrap.

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

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