help with polynomial

One factor of this polynomial is (2x − 1). 2x^3+5x^2-27x+12. Use long division to determine which expression represents the other factor.

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$(2x^3+5x^2-27x+12)$ : $(2x-1)$ = $x^2+3x-15$ 

$\underline{2x^3-\ x^2}$

            $6x^2-\ 27x$

            $\underline{6x^2\ +\ 3x}$

                     $-30x +\ 12$

                     $\underline{-30x+15}$

                                    $-3$

$(2x^3+5x^2-27x+12)$ = $(x^2+3x-15$ - $\large \frac{3}{2x-1}$) $\times (2x-1)$ 

  !