Polemic is a noun referring to a controversial argument hostilely refuting a specific belief or opinion. Polemical is an adjective meaning of or relating to controversy, refutation, or hostile argument. The words were variants of each other when they came to English from the French polémique (both around the early 17th century), but they have differentiated over time.
A person who writes a polemic is a polemicist, though polemist appears occasionally. The words’ corresponding adverb is polemically.
The novel was not a polemic, railing at the societal pressures keeping women in the kitchen. [NPR]
Opponents to having gay men serve openly in the military often recite the polemic that gay men lack masculine prowess. [Sydney Morning Herald]
But this is the opposite of a tired polemic about the pitfalls of stay-at-home motherhood. [Telegraph]
There is no polemical grandstanding going on, no bombast. [Financial Times]
For this reason, the Supreme Court decisions in cases that engage the public’s attention will often stir a polemical response. [The New Republic]
The film loses polemical bite towards the end but it doesn’t detract from its serious intent. [New Zealand Herald]