How did the advent of cotton factories shape American economic trends?

When you talk about "cotton factories," I assume you are
referring to textile factories like the ones at Lowell, MA.  The creation of these
factories did not, by themselves, change the US economy.  However, they were the first
steps in industrialization and industrialization was a huge
influence on economic trends in the US.

The major change
that came with industrialization was that workers really lost control of their labor and
the fruits of that labor.  Before the factories were created, much of the work of
America was done in people's homes by families and perhaps a few apprentices and other
helpers.  The work was relatively skilled and a large percentage of artisans were or
could expect to become their own bosses.

As
industrialization continued, however, work became something that was relatively
unskilled and was done outside the home.  Instead of becoming a cobbler and making
shoes, a person might become a worker in a shoe factory, working when they were told to
work and not doing anything that required great skill.  This was a major economic trend
that came about after the textile factories started the US towards
industrialization.