The force acting on a particle is related to the potential energy through the equation F(x) = -dU(x)/dx, where U(x) is the potential energy. In this question, the force is given as F(x) = Ax^2 - Bx.

To find the potential energy, we can integrate the force with respect to x.

Integrating F(x) = Ax^2 - Bx with respect to x, we get U(x) = (A/3)x^3 - (B/2)x^2 + C, where C is the constant of integration.

However, since potential energy is defined up to a constant, we can set C = 0.

Therefore, the potential energy of the particle is U(x) = (A/3)x^3 - (B/2)x^2.

Looking at the options:

Option 1: 2Ax - B. This is not the correct potential energy, as it is a linear function of x, while the potential energy should be a cubic function of x.

Option 2: -(2Ax - 3B)/6. This is the correct potential energy, which matches the result we obtained by integrating the force.

Option