Books with huge collections of hard, and original, problems on High School & Olympiad-level l Algebra?

Question

I'm searching for great and unknown books with huge collections of hard and original problems for my students on High School Algebra or Olympiad level Algebra, related (but not limited) to factoring polynomials and identities.

What I need is a huge collection of hard and unseen problems in high school algebra, because unfortunately most of the problems in these books below are well-known to my students and cannot feed their hunger. My students are about 13 and 14, are really talented.

• Problem Solving Strategies by Arthur Engel

• 101 Problems in Algebra by Titu Andreescu and Zuming Feng

• Introduction to Algebra by Richard Rusczyk

Answer 1

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

If not, then you can look at Problem-Solving Strategies by Engel. 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 Compendium. It contains some interesting algebra problems.

Answer 2

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.

Answer 3

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.

Answer 4

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