DIVISIVE - tending to cause disagreement or hostility between people. "the highly divisive issue of abortion" CONTROVERSIAL - giving rise or likely to give rise to controversy or public disagreement. "years of wrangling over a controversial bypass" CONTENTIOUS - causing or likely to cause an argument; controversial. "a contentious issue"

As I see it the following are the differences, but I am not claiming certainty. Divisive is something or someone that causes disagreement or antagonism between people (for example in Britain, Brexit) It is about causing division and separation. Controversial is also someone or something that causes disagreement or debate, but is not about causing division. It is more about arousing discussion of opposing opinions (For example - Trump saying 99% of Covid-19 cases are totally harmless). Contentious involves or is likely to lead to debate or controversy, whereas controversial intentionally or not arouses debate or controversy.

If u cant distinguish some differences amid some words, the first thing that you have to look up the English-English dictionary.