Polynomials Basics

Study Notes

Definition

A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication.

Characteristics

A polynomial can have any number of terms, but it cannot have variables in the denominator.
The variables in a polynomial are raised to non-negative integer powers.
Coefficients can be any real numbers, including fractions and decimals.

Types of Polynomials

Monomial: A polynomial with only one term.
Binomial: A polynomial with two terms.
Trinomial: A polynomial with three terms.

Operations with Polynomials

Addition and Subtraction: Combine like terms by adding or subtracting their coefficients.
Multiplication: Multiply each term in one polynomial by each term in the other polynomial, then combine like terms.

Properties of Polynomials

Commutative Property: The order of the terms in a polynomial does not change its value.
Associative Property: The order in which polynomials are added or multiplied does not change the result.
Distributive Property: A polynomial can be distributed over addition or subtraction.

Factors of Polynomials

Greatest Common Factor (GCF): The largest polynomial that divides two or more polynomials.
Factoring Out the GCF: Divide each term of a polynomial by the GCF to simplify the expression.

Important Concepts

Degree of a Polynomial: The highest power of the variable in a polynomial.
Leading Coefficient: The coefficient of the term with the highest power of the variable.
Roots of a Polynomial: The values of the variable that make the polynomial equal to zero.

Description

Learn about the definition, characteristics, and types of polynomials, as well as operations, properties, and factors of polynomials. Understand important concepts like degree, leading coefficient, and roots of a polynomial.