# What Is a Polynomial?

A polynomial is an algebraic expression in which terms are separated using the "+" and "-" operators. In this guide, you will learn more about the definition of a polynomial and its properties.

A polynomial is a kind of expression. An expression is a mathematical statement without an equal-to sign \((=)\).

**Related Topics**

- How to Write Polynomials in Standard Form
- How to Add and Subtract Polynomials
- How to Do Operations with Polynomials

**A step-by-step guide to** **polynomial**

A polynomial is a type of algebraic expression in which the exponents of all variables must be a whole number. The power of variables in any polynomial must be a non-negative integer. A polynomial contains constants and variables, but we can not perform division operations by a variable in polynomials.

The following image shows all the terms in a polynomial:

**Terms of a polynomial**

Polynomial terms are defined as parts of an expression that are separated by the operators \(+\) or \(-\). For example, the polynomial expression \(5x^3-\:4x^2+\:8x\:-12\) consists of four terms.

**Degree of a polynomial**

The highest or greatest power of a variable in a polynomial is known as the degree of the polynomial. The degree is used to determine the maximum number of solutions of a polynomial equation.

**Note: **The degree of a polynomial with more than one variable is equal to the sum of the power of the variables in it.

**Types of polynomials**

Polynomials can be categorized based on their degree and power. Based on the number of terms, there are mainly three types of polynomials listed below:

- Monomials
- Binomials
- Trinomials

A** monomial** is a type of polynomial with a single term. For example, \(x\), \(-4xy\), and \(7z^2\). A** binomial** is a type of polynomial that has two terms. For example, \(x + 3\), \(y^2+5\), and \(2x^3- 6\). While a **trinomial** is a type of polynomial that has three terms. For example \(3x^2+ 7x -5\), \(x + y + z\), and \(4x + y- 8\).

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