Chapter Twenty of Harry Potter and the Half-Blood Prince is called “Lord Voldemort’s Request.” Harry and Ron get out of the hospital on Monday and they go to breakfast with Hermione. On the way she explains that Ginny and Dean had a fight about Dean laughing at McLaggen hitting a bludger at Harry. Harry likes the idea that the two might be breaking up, as he still has a secret crush on Ginny. At breakfast it seems Ron and Lavender are also about to break up.
Harry goes to another lesson with Dumbledore. As he arrives Professor Trelawney is about to leave. Dumbledore is disappointed that Harry has been distracted by Malfoy and has not spent much effort at getting the true memory from Slughorn about the Horcruxes. He then says he has two last memories to show Harry.
Before they go into the memories Dumbledore explains how Voldemort left Hogwarts. He explains how many had high expectations for Voldemort in his seventh year that Slughorn tried to get him interested in working at the Ministry of Magic. Voldemort, however, ended working at Borgin and Burkes. Dumbledore explains that Voldemort’s first job choice was to be a professor at Hogwarts teaching Defense Against the Dark Arts. Dumbledore thinks he wanted to because he was attached to Hogwarts, wanted to continue to find the secret ancient magic in the castle, and he would have influence over young witches and wizards. The headmaster at the time (Professor Dippet) told Voldemort no, but to reapply in a few years. Dumbledore warned against ever hiring Voldemort.
Working for Borgin and Burkes Voldemort was sent to obtain treasures to sell in the shop and he had a skill for getting people to part with their items. At this point Harry and Dumbledore go into the memory of Hokey the house elf. The memory is of Voldemort visiting Hokey’s master (Hepzibah Smith) to make an offer on goblin armor. Hepzibah trusts Voldemort to see her most prized possessions as long as he does not tell Mr. Burke she has them.
The house elf brings the items in leather boxes. Inside one box is a golden cup with a badger on it, which means it was Helga Hufflepuff’s. Inside the other is something she had bought from Burke. It is golden locket with an S (i.e. the locket that Voldemort’s mother sold to Burke when she was pregnant with him).
Back in Dumbledore’s office Dumbledore explains that Hepzibah was found poisoned two days later. The house elf took the fall, as she remembered putting something the cocoa that turned out to not be sugar, but rather a rare poison. Dumbledore suspects it was Voldemort again changing memories and having another take the fall for the murder. The woman’s family did not find out about the missing possessions until much later and by then Voldemort had left the shop and disappeared.
There is a ten year gap between that memory and the last Dumbledore has to show Harry. The last memory belongs to Dumbledore. The memory is of Voldemort coming to visit Dumbledore, who is already the Headmaster in this memory. He had come to ask once again to be a teacher at Hogwarts. Dumbledore refuses because he thinks that Voldemort will try to get students to become Death Eaters, which exist by now, but Voldemort did not expect Dumbledore to know about. Dumbledore wanted the Defense Against the Dark Arts job and ever since he was refused Dumbledore has not been able to keep a professor in that job for more than a year. Dumbledore does not divulge why he thinks Voldemort might have come back to ask for the job. He says he will after Harry gets the true Horocrux memory from Slughorn.