Polynomials

What are Polynomials?

Adding & Subtracting Polynomials

Multiplying Polynomials

Polynomial Long Division

Factoring Polynomials: GCF and Grouping

Synthetic Division and The Remainder Theorem

The Factor Theorem and Rational Root Theorem

Descartes' Rule of Signs and Upper/Lower Bounds

Properties of Polynomial Roots: Vieta's Formulas and Multiplicity

Finding All Zeros of Polynomials (Real and Complex)

Graphing Polynomial Functions

Solving Polynomial Equations and Inequalities

Polynomial Modeling and Applications

Polynomial Transformations and Their Effects on Graphs

Solving Systems of Polynomial Equations

Polynomial Interpolation: Lagrange and Newton Forms

Numerical Methods for Approximating Real Roots (Bisection and Newton's Method)

Approximation with Polynomials: Conceptual Introduction to Taylor Series

Introduction to Orthogonal Polynomials (Legendre, Chebyshev)