The clean answer
Buddhism is non-theistic. Monotheism means one creator God at the center of worship; polytheism means many gods running the world's departments. Buddhism has neither arrangement: no creator, no god whose favor liberates you, and a founder who was a human teacher, not a deity. Liberation (nirvana) comes from insight and practice, not from divine grace, which removes the job that gods hold in theistic religions.
But what about the Buddhist 'gods'?
Buddhist cosmology does include devas: god-like beings living long, pleasant lives in higher realms. The catch that settles the classification: devas are mortal (they die and are reborn like everyone else), they didn't create the world, and they can't liberate you; in the old texts they sometimes come to the Buddha for teaching. Beings above you in comfort but beside you in samsara don't make a religion polytheistic, any more than believing in angels would. The wheel of rebirth (covered in the religion-or-philosophy question) turns for them too.
What the Buddha said when asked
Asked the great metaphysical questions (is the universe eternal, does a creator exist), the Buddha famously declined them as unhelpful: the parable of the poisoned arrow says a wounded man doesn't demand the archer's biography before treatment. Suffering is the wound; the path is the treatment; creator-questions don't change the medicine. That pragmatic silence is why Buddhism could travel through theistic and non-theistic cultures alike, absorbing local gods as decoration without ever needing them as engine.
Why this matters beyond the exam answer
The classification explains Buddhism's odd modern portability: a tradition whose core runs without a god can be practiced by theists, atheists, and everyone between, which is exactly what happened in the West. The branches differ in texture (Tibetan practice is rich with figures; Zen is nearly bare); the beginner's guide maps them, Taoism vs Buddhism handles the neighbor comparison, and the tradition's own voices run one page a day in 365 Days of Zen (★4.6 across 64 Amazon ratings), no theology prerequisite.
Common questions
Is Buddhism monotheistic, polytheistic, or non-theistic?
Non-theistic: it has no creator God (ruling out monotheism) and its god-like beings, devas, are mortal fellow-travelers rather than worshipped world-runners (ruling out polytheism in the meaningful sense). Liberation comes from practice, not divine favor.
Who are the gods in Buddhism then?
Devas: long-lived, fortunate beings in higher realms of the rebirth cycle. They didn't create the world, they still die, and they can't grant enlightenment; in the early texts they're sometimes students of the Buddha. Comfortable neighbors, not deities in the Western sense.
Is the Buddha a god?
No, and he said so: he presented himself as an awakened human teacher. Later devotional traditions honor him with god-adjacent reverence, but the doctrine is consistent that Buddhahood is a human achievement, which is the whole point: the path is walkable.
Is Buddhism universalizing or ethnic?
Universalizing: it's open to anyone regardless of birth, and it spread across Asia (and now the world) by conversion and teaching rather than descent, which is why it's classed with Christianity and Islam on that axis despite sharing no theology with them.