117 Polynomial Problems from the Awesomemath Summer Program (XYZ)

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
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