A. Construction of railways
B. Technical fairs
D. Control of banking
E. Factory construction
I think you could argue tha both gontrol of banking and education could be correct. I am pretty certain that government really had no concern for banks and how they were ran at that time. I don't think there was a real push for education until after the Industrial Revolution, most factories employed children during this time.
I am sure that this question can be debated. For example, during the industrial revolution did the government really encourage education? I suppose it did, but to what degree? It is hard to say. In view of this, some may say no, especially, if one has different definitions of education. And one can argue that some school took shape during this time to fight the influences of the industrial revolution. I can also see that D could be a possible answer, perhaps the best answer. I say this, because banks pretty much had free control. It is usually only during hard economic times (such as ours) that the government steps in to regulate.
Finally, when you say the West, this is pretty broad, since it includes all of North America and Europe.
If we define the period from 1700 to 1900 as roughly the Industrial Revolution in Europe and North America, Western governments were ill prepared to respond effectively to the impact of the changes that Industrialization brought forth. Only in the latter half of this time period, and continuing into our own day, did government take comprehensive and intrusive control. Government was not the catalyst that brought forth the benefits and difficulties of industrialization; government did not build railways and factories; that was done by individuals freely pooling their resources and freely able to engage in such projects. Banking, as we understand it, began when individuals began to pool money and spend it in research and development as they saw fit, not when government said "let there be banking." At least in the US, education was a function of and funded by the local community, not a program from Washington. If by "encouragement" is meant "regulation", government did not engage in regulation until it had expanded enough in all areas of life to do so, and once there were enough bureaucracies, they regulated with a vengeance. That we would look back and assume that government "lent a helping hand" and "encouraged" the Industrial Revolution is to widely miss the mark of historical accuracy.
Without a doubt, industrial- driven governments were not very big on the control of banking. I think that, even if the government wished to do so, the pervasive and powerful impact of economic progress and growth under industrialization would have dissuaded it. Some would argue that Western governments' industrial advocacy of education was to embrace a model of learning which permitted individuals full compliance to a system that would be appropriate to furthering industrial aims and the notion of maintaining the Status Quo. The educational model of many of these nations were "full of fact, little of fancy," to embrace Dickens' model of Coketown. This helps industrialists as it emphasizes technical modes of learning which can be easily manipulated into the factory life. Western governments were not very strong advocates of developing an educational system which sought to transform the issues of power and control, ideas that would pose a direct threat to the industrial base which proved to be so profitable to many in power.
The answer that is most likely to be correct here is D, if by "control of banking" you mean government control of banking.
During the Industrial Revolution, railroad and factory construction were high on the list of things that governments wanted to do. Education was important to promote a more scientifically capable elite. Technical fairs helped disseminate ideas.
By contrast, government control of banks was not in line with the ideas of the time. This was a time where government was supposed to help big business, not try to control it.