Which of the following describes the zeroes of the graph of f of x is equal to negative x to the 5th power plus 9 x to the 4th power minus 18 x cubed ?

Factor the polynomial: f(x) = −x³(x² − 9x + 18) = −x³(x − 3)(x − 6). The zeroes are x = 0, x = 3, and x = 6. Since x = 0 comes from the factor x³, it has multiplicity 3; the other two zeroes each have multiplicity 1. This matches the choice stating 0 with multiplicity 3, 3 with multiplicity 1, and 6 with multiplicity 1.

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