Which statement describes the graph of f(x) = –x4 + 3x3 + 10x2?

Factor the polynomial: f(x) = −x²(x² − 3x − 10) = −x²(x − 5)(x + 2). The zero at x = 0 has multiplicity 2, so the graph touches the x-axis there; the zeros at x = 5 and x = −2 have multiplicity 1, so the graph crosses at both. Thus, the correct choice is B: it touches at 0 and crosses at 5 and −2.

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