What is a critical analysis of a text?

https://www.quora.com/What-is-a-critical-analysis-of-a-text

This could mean a number of different things:

1.  Old-school vague English teacher sort of assignments that don't go into any more detail or depth than to "critically analyze" a text.  What this seems to mean is to take apart individual lines or quotes and interpret them--as in a poem, for example.  It's not necessarily saying to apply a particular technique or theory to your interpretations, just tell the teacher what you think they mean or why the author put it there.  It's not even really saying to justify why you think it means what you think it means, just say what you think, give it your best shot.  If you think something symbolizes the author's lonely desperation or unspoken desires, go for it.  No one will actually call you to task for making outrageous, totally unfounded assertions that could never hope to be proven with anything approaching real evidence.  These types of assignments are usually met with an appreciative "interesting analysis" sort of response that is as vague as the assignment itself was.

2.  If you're taking a class from a postmodern, proto-Marxist, critical theorist type, it most likely means to investigate a text and show how it either collapses into indeterminate meanings (the Derrida deconstruction school), instantiates transgression (queer theory), exposes bourgeois manipulation of the marketplace and hegemony (Marxist, obviously), posits gender category crisis (queer theory again, possibly feminist theory), de-colonizes subalterns (Post-Colonial theory) etc.  Basically, this type of assignment is seeing how well you know the theory and can apply it and (it's implied) can tow the party line.  It's assumed that the theories are brilliant exposés of patriarchal, hegemonic, reactionary cultural practices and you, the brilliant critical theorist, have all the tools ready at your disposal for dismantling them.  Never mind that nothing viable is offered in their place.  Once the Western tradition has been exterminated, they'll think about what to do next. 

3.  Last but certainly not least, you may actually be expected to delineate premises and conclusion(s) in an argument, state any underlying assumptions, expose fallacious reasoning, evaluate evidence, and/or posit counterarguments with counterexamples.  This is the kind of thing you would see on the GRE writing exam where an issue is presented and you must take it apart using old-fashioned logical analysis and sound reasoning and not the trendy pomo theory du jour mentioned above.  Alternately, you could be discussing an issue and attempting to persuade a reader that your proposed solution should be taken seriously because you have carefully considered the evidence, the alternatives, the pros and cons and can cogently put it all together in a compelling argument.

So like I said, depends.