Final answer:
Government subsidies were the critical factor in encouraging railway companies to construct tracks through the West, offering the necessary financial resources that private companies lacked to undertake such expansive projects.
Step-by-step explanation:
The most important factor in motivating railway companies to build track through the uninhabited territories in the West was government subsidies.
The United States government played a crucial role in the expansion of the railway network by providing land grants and financial incentives to railroad companies through legislation such as the Pacific Railway Act.
These government subsidies were vital because they essentially provided the resources needed to finance the construction of such massive infrastructure projects, which private enterprises alone could not afford.
Subsidies not only encouraged the construction of the railways but also helped to establish a more unified nation by connecting various regions and promoting economic development.