---
title: Polynomials
description: Polynomials are algebraic expressions consisting of variables and coefficients combined using addition, subtraction, and multiplication. Learners will understand polynomial arithmetic, factoring techniques, and root-finding methods to analyze and graph polynomial functions of various degrees.
category: mathematics
subcategory: algebra
difficulty: beginner, intermediate, advanced
url: /subject/polynomials
---

# Polynomials

Polynomials are algebraic expressions consisting of variables and coefficients combined using addition, subtraction, and multiplication. Learners will understand polynomial arithmetic, factoring techniques, and root-finding methods to analyze and graph polynomial functions of various degrees.

## Available Resources

1 Books • 2 Courses • 4 Websites

## Websites

### 1. Purplemath

Purplemath lesson on the end behavior of polynomial graphs: how degree parity and the sign of the leading coefficient determine whether each end rises or falls. Worked examples let students sketch or match a polynomial's graph without plotting points.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://www.purplemath.com/modules/polyends.htm

**Tags:** polynomials, end-behavior, polynomial-graphs, leading-coefficient, algebra

### 2. Art of Problem Solving

Art of Problem Solving wiki reference on polynomials as used in competition mathematics: degree, coefficients, roots and the Fundamental Theorem of Algebra, with links to related results such as Vieta's formulas and to contest problems for practice.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://artofproblemsolving.com/wiki/index.php/Polynomials

**Tags:** polynomials, competition-math, vietas-formulas, polynomial-roots, algebra

### 3. Wolfram MathWorld

**Author:** Eric W. Weisstein

MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://mathworld.wolfram.com

**Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry

### 4. mathsisfun.com

MathIsFun.com is a beginner-friendly math site that explains concepts with clear, step-by-step lessons and interactive activities. It covers topics from algebra and linear equations to geometry, fractions, data, and more, with practice problems, worksheets, and quizzes.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://mathsisfun.com

**Tags:** websites, mathematics-statistics, algebra

## Courses

### 1. Algebra 1

**Author:** Sal Khan

Complete school Algebra 1 course of video lessons and graded practice covering linear equations and inequalities, graphing, functions, systems of equations, exponents, polynomials and quadratics. Learners finish able to solve and graph linear and quadratic problems and read function notation.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://www.khanacademy.org/math/algebra

**Tags:** algebra, linear-equations, functions, systems-of-equations, quadratic-equations

### 2. Algebra: Elementary to Advanced - Polynomials and Roots

**Author:** Joseph W. Cutrone

Third course in Johns Hopkins's algebra sequence, covering exponential functions, polynomial arithmetic and factoring, square and nth roots, and percent and interest applications. Finishes with a cumulative exam, preparing you for precalculus, statistics or data science coursework.

**Difficulty:** Beginner | **Language:** English | **Price:** Free

**Link:** https://www.coursera.org/learn/polynomials-roots

**Tags:** polynomials, factoring, exponents, radicals, algebra

## Books

### 1. Algebra for College Students

Algebra for College Students - A book resource

**Difficulty:** Intermediate | **Language:** English | **Price:** Paid

**Link:** https://www.amazon.com/dp/0130328391?tag=edmonddante07-20

**Tags:** books, mathematics-statistics, algebra

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