Polynomials (original) (raw)
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.
Parts of a polynomial
**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.
For Programmers
Practice using the code in your preferred programming language.