Which of the following describes the roots of the polynomial function f of x is equal to open paren x plus 2 close paren squared times open paren x minus 4 close paren times open paren x plus 1 close paren cubed ?

Set each factor equal to zero to find the roots. The factor (x + 2)² gives root −2 with multiplicity 2, (x − 4) gives root 4 with multiplicity 1, and (x + 1)³ gives root −1 with multiplicity 3. These roots and multiplicities match choice D.

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