Polynomials

Polynomials are mathematical expressions made up of variables (like x, y, etc.), constants (numbers), and exponents (which are non-negative integers). These expressions are combined using addition, subtraction and multiplication operations.

Real-Life Examples:

• Area of a square field with variable side: A = s²
• Area of a rectangle with changing dimensions: A = (x+2)(x+3) = x² + 5x + 6
• Height of a thrown ball: h(x) = -x² + 10x + 5
• Volume of a cube depends on side: V = x³

Foundations

Covers the basic concepts and definitions of polynomials.

• Introduction to Polynomials
• Degree of a Polynomial
• Types of Polynomials
• Polynomials in One Variable
• Polynomial Formula
• Polynomial vs Algebraic Expressions

Basic Operations & Identities

Explains how to perform operations on polynomials and use algebraic identities.

• Addition and Subtraction of Polynomials
• Multiplication of Polynomials
• Division of Polynomials
• Polynomial Identities

Factorization & Theorems

Focuses on factoring polynomials and understanding key theorems.

• Factorization of Polynomials
• Methods of Factoring Polynomials
• Remainder Theorem
• Factor Theorem
• Polynomial Division Algorithm
• Synthetic Division

Zeroes & Roots

Deals with the roots of polynomials and their relationships with coefficients.

• Zeroes of a Polynomial
• Relationship between Zeroes and Coefficients
• Geometrical Meaning of Zeroes
• Vieta's Formula
• Nature of Roots

Polynomial Equations (Advanced)

Covers advanced methods for solving polynomial equations and analyzing roots.

• Solving Higher Degree Polynomials
• Multiplicity of Roots
• Polynomial Functions
• Graph of Polynomial Functions
• Applications of Polynomials in Real Life

Practice

Provides practice questions to improve understanding of polynomials.

• Practice Questions on Polynomials
• Zeros of Polynomial Practice Problem

For Programmers

Practice using the code in your preferred programming language.

• Program to add two polynomials
• Adding two polynomials using Linked List
• Multiply two polynomials