Factorizing $12x^3 - 8x^2 - 3x + 2$

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How should I factorize this cubic expression?

$$12x^3 - 8x^2 - 3x + 2$$

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We observe that $12:8=3:2$

So

$\begin{array} 112x^3 - 8x^2 -3x + 2 \\ &=&4x^2(3x-2) - (3x-2) \\ &=&(3x-2)(4x^2 - 1)\\ &=&(3x-2)((2x)^2 - 1^2)\\ &=&(3x-2)(2x+1)(2x-1) \\ \end{array}$