The correct answer to this open question is the following.
Although there are no options attached, we can say the following.
The historical factor that contributed to the increase in labor union membership from 1865 to 1900 was the many injustices committed by the owners of the industries during the so-called Gilded Age.
In those years, teh Ribber Barons of America such as Jhon F. Rockefeller or Andrew Carnegie had created monopolies with their huge companies; the Standard Oil Company and teh Steel Company, respectively. American workers labored in these industries under unhealthy conditions, for long hours and low salaries. That is why most of these workers joined labor unions from 1865 to 1900.