Andreescu T. 117 Polynomial Problems. From the Awesomemath Summer Program 2019

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Andreescu T. 117 Polynomial Problems. From the Awesomemath Summer Program 2019

Textbook in PDF format The ubiquity of polynomials and their ability to characterize complex patterns let us better understand generalizations, theorems, and elegant paths to solutions that they provide. We strive to showcase the true beauty of polynomials through a well-thought collection of problems from mathematics competitions and intuitive lectures that follow the sub-topics. Thus, we present a view of polynomials that incorporates various techniques paired with the favorite themes that show up in math contests. Preface Basic Properties of Polynomials - Part I Identities The coefficients of xd in polynomial products Factoring and its implications Values of polynomials Division, GCD of polynomials The composition of polynomials Odd and even polynomials Basic Properties of Polynomials - Part II Polynomial roots Integer and rational roots of polynomials Intermediate value theorem, increasing and decreasing polynomials Second degree polynomials The form ax2+bx+c The Discriminant Roots Vieta's formulas Solving Inequalities Miscellaneous problems More advanced problems Third degree polynomials Roots and graph Vieta's formulas More advanced problems Fourth degree polynomials Solving equations Vieta's formulas Number of real roots and graph Miscellaneous On roots of polynomials - elementary problems Vieta's formulas in the general case Inequalities between coefficients and roots Miscellaneous problems Number theory and polynomials Number theory and low degree polynomials P(a)-P(b) Introductory problems Advanced problems Solutions to introductory problems Solutions to advanced problems Other Books from XYZ Press