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I'm searching for hard and creative problems in basic algebra related (but not limited) to factoring polynomials and identities for my students.

Iv'e collected problems in these books, but what I need is a huge collection of hard and unseen problems in high school algebra:

-Problem Solving Strategies by Arthur. Engel

-101 Problems in algebra by Titu Andreescu and zuming Feng

-Introduction to Algebra by Richard Rusczyk

unfortunately most of the problems in those books are well-known to my students and cannot feed their hunger...

I should mention that my students are about 13 and 14 and are really talented and most of them know those books.

I'm looking for great and unknown books with huge collections of hard and original problems on High School Algebra or Olympiad level Algebra...

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Challenging Problems in Algebra by Alfred S. Posamentier and Charles T. Salkind (Dover) would certainly fit your needs.

If not then you can look at Engel - Problem-Solving Strategies, it has a section on polynomials which contains 82 problems.

Another option is 101 Problems in Algebra From the Training of the USA IMO Team by Titu Andreescu, Zuming Feng. You could also take a look at the IMO Compedium, it contains some interesting algebra problems.

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  • $\begingroup$ I've seen this book I mean something different. sth like olympiad or pre-olympiad level algebra problems $\endgroup$ – souran Feb 8 '15 at 19:49
  • $\begingroup$ @mmahdit I suggested two other books in my recent edit. $\endgroup$ – Workaholic Feb 8 '15 at 20:21
  • $\begingroup$ thanks for both books I meant sth stranger because most of my students have read the second one. Engel's book is in hands of most of them and I myself enjoyed reading it years ago when I was student. Thanks again for your kind help :) $\endgroup$ – souran Feb 8 '15 at 20:23
  • $\begingroup$ @mmahdit What about the third one? $\endgroup$ – Workaholic Feb 8 '15 at 20:24
  • $\begingroup$ the 3rd one is a great book and I've read it when I was student. I mean sth like problems of the first chapter of this book. $\endgroup$ – souran Feb 8 '15 at 20:27
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I think you'll find Polynomials by E.J. Barbeau to satisfy your request very nicely indeed. It's probably the most exhaustive source on this topic for beginners and contains an enormous wealth of exercises. It's also extremely clear and gives many insights into the theory of polynomials at this level,mostly without abstract algebra.More sophisticated aspects of polynomials which require basic ring and field theory are discussed in optional sections.

I think you'll find this book just what the doctor ordered.

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  • $\begingroup$ op's students might have seen it and may be aware of it. $\endgroup$ – abel Feb 8 '15 at 20:55
  • $\begingroup$ ok,but didn't see anything that indicated that. $\endgroup$ – Mathemagician1234 Feb 8 '15 at 22:58
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Have you looked at Art of Problem Solving's community? You can either search for "polynomial" and cherry pick the problems you like, or just go to the olympiad section for algebra. You'll find all levels there.

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  • $\begingroup$ It's been years that I'm checking that website but it takes along time to cherry pick those problems.you asked about their age: they are about 13-14 and they are highly talented. some of them are really gifted and sometimes I find a genius among them. So I'm deeply responsible to those talents. $\endgroup$ – souran Feb 8 '15 at 20:57
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One resource that I use from time to time is Leonhard Euler's Elements of Algebra. There aren't a lot of practice problems, but some of the ones that he does have are somewhat difficult. As an example, take a look at problem 12 on this page. https://archive.org/stream/elementsalgebra00lagrgoog#page/n277/mode/2up

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