What is the completely factored form of f(x) = 6x3 – 13x2 – 4x + 15?

Group the terms: 6x³ − 13x² − 4x + 15 = (6x³ − 9x²) + (−4x² + 6x) + (−5x + 15), which factors to 3x²(2x − 3) − 2x(2x − 3) − 5( x − 3)? Instead, test x = −1: f(−1) = 0, so x + 1 is a factor. Dividing gives 6x² − 19x + 15 = (2x − 3)(3x − 5). Therefore the completely factored form is (x + 1)(2x − 3)(3x − 5), choice D.

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