Polynomials Terminology and Factorization

Introduction

• Terminology of polynomials and their role
• Importance of polynomials in math such as graphs, algebraic expressions, etc.
• Explanation of constants and variables

General Form of Polynomials

• General nomenclature and form of polynomials
• Degree, terms, and value of polynomials

Types of Polynomials

Based on Number of Variables

• Single Variable: Polynomials with one variable
• Multiple Variables: Polynomials with two or more variables (e.g., x and y)

Based on Number of Terms

• Monomial: Polynomials with a single term
• Binomial: Polynomials with two terms
• Trinomial: Polynomials with three terms

Based on Degree

• Constant Polynomial: Polynomials with degree 0
• Linear Polynomial: Polynomials with degree 1
• Quadratic Polynomial: Polynomials with degree 2
• Cubic Polynomial: Polynomials with degree 3
• Bi-quadratic Polynomial: Polynomials with degree 4

Value of a Polynomial

• Method to find the value of a polynomial
• Calculation of specific values at specific variables

Factor Theorem

• Use of the factor theorem
• Finding factors using the factor theorem

Zeros of a Polynomial

• Meaning of zeros of a polynomial and method to find them
• Example: Quadratic and cubic polynomials

Methods of Factorization

Middle Term Splitting Method

• Factorization of quadratic polynomials
• Step-by-step method
• Example

Factor Theorem

• Finding factors of cubic polynomials
• Verification using the factor theorem
• Example

Algebraic Identity

• Important formulas and their recognition
• Use of formulas in factorization and solving

Conclusion

• Importance of polynomials and their various uses
• Review of different terminologies, types, and factorization methods