The word facetious describes something you don't take seriously. Remove the middle "e," and factious describes a dissenting group. And finally there's fatuous, which is a fancy way to say dumb.
Someone who is facetious (fuh-see-shus) is only joking. If you tell your mom you want Brussels sprouts with every meal, make sure it's clear you're being facetious if you actually don't like Barbie cabbage. Facetious remarks are sometimes inappropriate too. Facetious in the wild:
"Granted, many of the Lent-related Twitter posts are likely facetious, so the list is to be taken with a grain of salt." (Time)
"If you're going to be facetious, really pour on the sarcasm so that hardly anyone could mistake your tone." (Forbes)
A factious (fak-shus) group disagrees with the mainstream and breaks off into a smaller group of angry rebels. A factious group doesn't have to be angry, but it helps. It's a word often used in politics -- in fact, it comes from the Latin factionem for "political party." Factious issues divide people. Examples:
"It was the arbitrary invention of a particular time and place — the factious and violent medieval church." (Time)
"He first of all required them to banish Fénelon from their house as being a factious and rebellious person." (Dawson, William LeSueur)
The word fatuous (fah-chus) means silly, foolish, and maybe a little bit smug. In a debate, you might call your opponent's response fatuous. Here are examples:
"They realized then what a silly, fatuous thing it was to do, going out and killing rare birds." (Scientific American)
"Not to mention his fatuous conflation of Marxism, Freemasonry and Judaism." (Salon)
Don't take anything facetious on its face because it's not serious. Reserve factious for factions. And fatuous? Totally foolish.