Factor x3 + 3x2 + 2x completely.

First factor out the greatest common factor, x: x³ + 3x² + 2x = x(x² + 3x + 2). The quadratic factors as (x + 1)(x + 2), because 1 · 2 = 2 and 1 + 2 = 3. Thus the complete factorization is x(x + 1)(x + 2), choice B.

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