This book is the first one in a three-book series and proposes a very detailed and
complete journey through the amazing world of polynomials.
This first volume successfully presents some of the basic properties of polynomials,
with emphasis on some factorings, on the division of the polynomials, on the odd and
even polynomials, as well as on the integer and rational roots of the polynomials. Also,
the volume discusses in a very methodical way the specific properties of the
polynomials of second, third and fourth degree, with a focus on Vieta’s formulas and
number of roots in each of these particular cases. Roots of polynomials are further
discussed with an accent on Vieta’s general formulas and other inequalities between
coefficients and roots.
All topics of the book are carefully explained from a theoretical point of view and many
examples are used to reinforce some of the concepts. Further on, the authors present
many significant problems that were used in several past mathematical competitions
from around the world with complete solutions and comments. Problems are carefully
selected and range in difficulty level from medium to hard.
The uniqueness of this book consist in the multitude of the algebraic techniques that
are explained and exposed in a very coherent way with an effort on creating a
continuum from the beginning to the end.
The part that I personally treasure in this the book is the section concerning number
theory and polynomials, with all the subsequent original proposed problems.
As the authors use to do in many of their books, this volume contains also two rich
sections of proposed problems : introductory and advanced. All problems have
detailed solutions and comments to guide the reader through the process of learning
and understanding the methods.
I strongly recommend this book to all the young minds that train for writing AMC 10-12,
AIME or USAMO tests, or to all other students that want to explore properties of
polynomials beyond the limits of the regular academical school curriculum. Also, the
book could be a very strong tool for teachers that work to train students for competing
in mathematical competitions.