Find the root(s) of f (x) = (x + 5)3(x - 9)2(x + 1).

A root occurs when one of the factors equals zero. Setting x + 5 = 0 gives x = −5 with multiplicity 3; setting x − 9 = 0 gives x = 9 with multiplicity 2; and setting x + 1 = 0 gives x = −1 with multiplicity 1. Therefore, the correct choices are −5 with multiplicity 3, 9 with multiplicity 2, and −1 with multiplicity 1.

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