HIV May Induce Rapid Cell Division in Some Cell Types

HIV may induce rapid cell division in some cell types. Would rapid cell division favor mutation and induction of possible cancerous lesions?

A) No-we have proofreading and repair capabilities in our DNA synthesis enzymes that prevent mutations. Just because more cell division is occurring doesn't mean more mutation would occur.
B) Yes-especially as all of these cells are infected with HIV as they are newly made. Since HIV integrates into the host cell chromosome, each time it does so it has a small chance to cause a cancerous state.
C) Yes-spontaneous mutation is a random event. Sometimes it is corrected, but rarely it goes forward. Technically, then, each and every new cell formed is a chance for induction of a cancerous state. If you increase the number of cells formed, you increase the chance for that induction event.
D) No-part of the HIV lifecycle also hijacks the DNA synthesis machinery. Since it's hijacked, there's no way that it could be used to produce mutations in the host cells that would lead to cancerous states.