Which polynomial function has a leading coefficient of 1 and roots open paren 7 plus i close paren and open paren 5 minus i close paren with multiplicity 1 ?

A root r gives a factor (x − r), so the stated roots contribute (x − (7 + i)) and (x − (5 − i)). For a polynomial with real coefficients, their conjugates, 7 − i and 5 + i, are roots too, giving the other two factors. Choice D contains all four factors, and each has leading coefficient 1, so their product has leading coefficient 1.

AI-written and checked against the verified answer.