$$\eqalign{
& 6{x^2} + x - 2 = 6{x^2} + ax - bx - 2 \cr
& a - b = 1 \Rightarrow a = b + 1 \cr
& \frac{6}{a} = \frac{b}{2} \Rightarrow ab = 12 \cr
& \Rightarrow a,b \in U(12) = \left\{ {1;2;3;4;6;12} \right\} \cr
& a = b + 1 \Rightarrow b = 3;a = 4 \cr
& 6{x^2} + x - 2 = 6{x^2} + 4x - 3x - 2 = 2x(3x + 2) - (3x + 2) = (2x - 1)(3x + 2) \cr} $$