Which of the following describes the roots of the polynomial function f of x is equal to open paren x minus 3 close paren to the 4th power times open paren x plus 6 close paren squared ?

Set each factor equal to zero. The factor (x − 3)^4 gives x = 3, with multiplicity 4, and (x + 6)^2 gives x = −6, with multiplicity 2. Therefore, the roots are 3 with multiplicity 4 and −6 with multiplicity 2, which is choice D.

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