Learn on PengiBig Ideas Math, Algebra 1Chapter 7: Polynomial Equations and Factoring

Lesson 1: Adding and Subtracting Polynomials

Property A polynomial is an algebraic expression with several terms. Each term is a power of a variable (or a product of powers) with a constant coefficient. The exponents in a polynomial must be whole numbers, which means that a polynomial has no radicals containing variables, and no variables in the denominators of fractions.

Section 1

What is a polynomial?

Property

A polynomial is an algebraic expression with several terms. Each term is a power of a variable (or a product of powers) with a constant coefficient.
The exponents in a polynomial must be whole numbers, which means that a polynomial has no radicals containing variables, and no variables in the denominators of fractions.

Examples

The expression $4x^3 + 2x^2 - 7x + 5$ is a polynomial.

The expression $2 + \frac{6}{x}$ is not a polynomial because a variable appears in the denominator.

Section 2

Types of Polynomials

Property

A monomial is an algebraic expression with one term. A monomial in one variable is a term of the form $ax^m$ , where $a$ is a constant and $m$ is a whole number.

Polynomials

polynomial—A monomial, or two or more algebraic terms combined by addition or subtraction is a polynomial.
monomial—A polynomial with exactly one term is called a monomial.
binomial—A polynomial with exactly two terms is called a binomial.
trinomial—A polynomial with exactly three terms is called a trinomial.

Examples

$5x^3 - 2x + 1$ is a trinomial because it has three terms.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

What is a polynomial?

Property

Examples

The expression $4x^3 + 2x^2 - 7x + 5$ is a polynomial.

The expression $2 + \frac{6}{x}$ is not a polynomial because a variable appears in the denominator.

Section 2

Types of Polynomials

Property

A monomial is an algebraic expression with one term. A monomial in one variable is a term of the form $ax^m$ , where $a$ is a constant and $m$ is a whole number.

Polynomials

polynomial—A monomial, or two or more algebraic terms combined by addition or subtraction is a polynomial.
monomial—A polynomial with exactly one term is called a monomial.
binomial—A polynomial with exactly two terms is called a binomial.
trinomial—A polynomial with exactly three terms is called a trinomial.

Examples

$5x^3 - 2x + 1$ is a trinomial because it has three terms.

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

What is a polynomial?

Property

Examples

The expression $4x^3 + 2x^2 - 7x + 5$ is a polynomial.

The expression $2 + \frac{6}{x}$ is not a polynomial because a variable appears in the denominator.

Section 2

Types of Polynomials

Property

A monomial is an algebraic expression with one term. A monomial in one variable is a term of the form $ax^m$ , where $a$ is a constant and $m$ is a whole number.

Polynomials

polynomial—A monomial, or two or more algebraic terms combined by addition or subtraction is a polynomial.
monomial—A polynomial with exactly one term is called a monomial.
binomial—A polynomial with exactly two terms is called a binomial.
trinomial—A polynomial with exactly three terms is called a trinomial.

Examples

$5x^3 - 2x + 1$ is a trinomial because it has three terms.