Is down syndrome dominant, recessive, polygenic inheritance, multiple alleles, sex linked, codominance, or incomplete dominance?

None of these. Extra chromosome. Your teacher should be able to explain why the others are wrong. .
Abn. cell division. Most cases of Down syndrome are not inherited. When the condition is caused by trisomy 21, the chromosomal abnormality occurs as a random event during the formation of reproductive cells in a parent. The abnormality usually occurs in egg cells, but it occasionally occurs in sperm cells. An error in cell division called nondisjunction results in a reproductive cell with an abn. number of chromosoms.