Which product of prime polynomials is equivalent to 3x4 – 81x?

Factor out the greatest common factor, 3x: 3x⁴ − 81x = 3x(x³ − 27). The expression in parentheses is a difference of cubes, and x³ − 3³ = (x − 3)(x² + 3x + 9). Thus the prime-polynomial factorization is 3x(x − 3)(x² + 3x + 9), which is choice B.

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