Polynomials (Problem Books in Mathematics)

The book extends the high school curriculum and provides a backdrop for later study in calculus, modern algebra, numerical analysis, and complex variable theory. Exercises introduce many techniques and topics in the theory of equations, such as evolution and factorization of polynomials, solution of equations, interpolation, approximation, and congruences. The theory is not treated formally, but rather illustrated through examples. Over 300 problems drawn from journals, contests, and examinations test understanding, ingenuity, and skill. Each chapter ends with a list of hints; there are answers to many of the exercises and solutions to all of the problems. In addition, 69 "explorations" invite the reader to investigate research problems and related topics.

From the reviews:

E.J. Barbeau

Polynomials

"This book uses the medium of problems to enable us, the readers, to educate ourselves in matters polynomial. In each section we are led, after a brief introduction, into a sequence of problems on a certain topic. If we do these successfully, we find that we have mastered the basics of the topic. If we have any difficulties, we can refer first to the hints, and, failing these, to the detailed solutions. These form an important and substantial part of the book, and often refer the reader on to the research literature. The book, like good literature, can be read successfully at different levels, and would not be out of place in any mathematician's library."―MATHEMATICAL REVIEWS

“This is a two-faced book, and that’s a good thing. One face is a set of enrichment materials for bright high school students. The other face is a fairly comprehensive textbook on algebraic properties of polynomials. ... The present book is an excellent introduction to the subject for anyone, from high schooler to professional.” (Allen Stenger, The Mathematical Association of America, August, 2011)