Final answer:
Tom Riddle discovers the term 'Horcrux' in the Hogwarts Library while researching as a student. The correct option is A.
Step-by-step explanation:
Tom Riddle first encountered the term 'Horcrux' while he was a student at Hogwarts. This revelation is provided in the Harry Potter series, specifically in the sixth book, 'Harry Potter and the Half-Blood Prince'.
In the story, Tom Riddle learns about Horcruxes through his research in the Hogwarts Library, where he stumbles upon the topic in the restricted section that contains dark and dangerous books.
He further explores this dark magic in great detail, eventually using this forbidden knowledge to split his soul and create multiple Horcruxes, all in his quest for immortality.