What Is a Polynomial?

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

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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 \(4x + y- 8\).