What would this mean:

identify the source of the quotation.

One of the quotes was:

"a house divided against itself cannot stand"

this is a quote that Abraham Lincoln said

would the source be Abraham Lincoln or the speech where he said it and where?

This is what I had to do, it states:

identify the source of the quotation, when and in what context it was used, and its larger significance in illuminating a theme of American history.

Yes, the source is Abraham Lincoln.

Here's how to cite a speech:
http://www.monroecc.edu/depts/library/mla.htm >> http://www.monroecc.edu/depts/library/mla.htm#lecture
(Use the "lecture" format, but use the word "speech" instead.)

what would: in what context it was used: mean?

How the quote was used?

For the same Lincoln quote would it be that it also meant that the country can't be half free and half slave?

From which of Lincoln's speeches does this come? Where was he when he gave the speech? To whom was he speaking?

Context

The context was a speech given to Republican convention delegates in Springfield, IL in 1858. It was used to show Lincoln's idealism and warn his listeners of the threat to the Union. You're correct about its meaning.

Here's some good background on this speech.

http://showcase.netins.net/web/creative/lincoln/speeches/house.htm

To identify the source of a quotation, you need to determine where it comes from, such as a book, article, speech, or interview. Here are some steps you can take to find the source:

1. Search online: Use search engines like Google to enter the exact quotation. Enclose the quote in quotation marks to narrow down the results. Look for any references or mentions of the quote on websites, blogs, or forums that might provide the source.

2. Check quotation databases: There are numerous online quotation databases where you can search for specific quotes. Some popular ones include BrainyQuote, Goodreads, and Wikiquote. Enter the quote into the search bar and see if the source is listed.

3. Consult books and reference materials: If the quote is well-known, it may be referenced in books or collections of quotations. Check popular quotation books or search library catalogs to find relevant sources.

4. Look for citations: If the quote was mentioned in an article or academic paper, there might be a citation or reference to the original source. Check footnotes, endnotes, or the bibliography for any references that could lead you to the source.

5. Identify the speaker: If the quote includes the name of the person who said it, you can search for that person's work, speeches, interviews, or books to find the original source.

By following these steps, you can find the source of a quotation and gain a better understanding of its context and authenticity.