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In China, there's a course called “Advanced Algebra," the first chapter of this course is all about polynomials, I wonder which undergraduate math books cover this topic? The details are below, sorry for the incorrect terminology, I used online dictionary for translation.

1.1 Number field
1.2 Polynomial of one indeterminate
1.3 Polynomial integral division
1.4 The greatest common divisor
1.5 The factorization theorem
1.6 Multiple factor
1.7 Polynomial function
1.8 The factor of complex coefficient in real coefficient polynomial decomposition
1.9 Polynomial with rational coefficients
1.10 Polynomial in several indeter minates
1.11 Symmetric polynomial

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up vote 1 down vote accepted

Here is The Khan Academy's offerings (online) for Polynomials. Related topics can also be found at the site's Algebra and Algebra II menu to the left of the linked webpage.

Perhaps more appropriate: Polynomials and Rational Functions are also discussed in the Khan Academy's Trigonometry and Precalculus offerings, discussed here at a more sophisticated level.

Perhaps this will serve as a handy resource.

ADDED: If, as your comments suggest, you are interested in polynomials, as they relate to abstract (modern) algebra: you might want to check out this online study guide (also available is a free text which the author has made accessible from the site), and the topics listed:

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With all respect,is that undergraduate level algebra? – Ave Maleficum Mar 31 '13 at 3:43
I am looking at the list you give of topics; perhaps the first link is too elementary, but the second link covers much of what you've written. – amWhy Mar 31 '13 at 3:52
Perhaps you are looking for "abstract algebra" related material with respect to polynomials? Rings, fields, etc? – amWhy Mar 31 '13 at 3:52
Thanks for the reply,I will check out"abstract algebra" – Ave Maleficum Mar 31 '13 at 3:55

You might consider the book "Polynomials" by E.J. Barbeau. This will give you all you'd ever like to know concerning polynomials in a clear, informative manner. Some undergraduate math experience is recommended.

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This is exactly the book I was going to recommend. It really does have everything one can possibly want to know about polynomials. A great read and a great reference. And a good chunk, at least in the beginning, is accessible by the OP. – Fixed Point Mar 31 '13 at 7:45

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