Which statement describes the graph of f(x) = 4x7 + 40x6 + 100x5?

Factor the polynomial: f(x) = 4x⁵(x² + 10x + 25) = 4x⁵(x + 5)². The zero x = 0 has multiplicity 5, which is odd, so the graph crosses the x-axis there. The zero x = −5 has multiplicity 2, which is even, so the graph touches the x-axis there. Therefore, choice C is correct.

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