Which statement describes the graph of this polynomial function? f of x is equal to x to the 5th power minus 6 x to the 4th power plus 9 x cubed

Factor the polynomial: f(x) = x³(x² − 6x + 9) = x³(x − 3)². The zero at x = 0 has multiplicity 3, which is odd, so the graph crosses the x-axis there. The zero at x = 3 has multiplicity 2, which is even, so the graph touches the x-axis there. This matches choice B: it crosses at 0 and touches at 3.

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