Which product of prime polynomials is equivalent to 4x5 – 6x4 + 4x3 – 6x2?

Factor out the greatest common factor, 2x²: 4x⁵ − 6x⁴ + 4x³ − 6x² = 2x²(2x³ − 3x² + 2x − 3). Group the terms inside: (2x³ + 2x) + (−3x² − 3) = 2x(x² + 1) − 3(x² + 1). Factoring out (x² + 1) gives 2x²(x² + 1)(2x − 3), which matches choice A.

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