Browse Definitions:
Definition

polynomial

A polynomial is a mathematical expression consisting of a sum of terms, each term including a variable or variables raised to a power and multiplied by a coefficient.  The simplest polynomials have one variable.  A one-variable (univariate) polynomial of degree n has the following form:

anxn + an-1xn-1 + ... + a2x2 + a1x1 + ax

where the a's represent the coefficients and x represents the variable.  Because x1 = x and x = 1 for all complex numbers x, the above expression can be simplified to:

anxn + an-1xn-1 + ... + a2x2 + a1x + a

When an nth-degree univariate polynomial is equal to zero, the result is a univariate polynomial equation of degree n:

anxn + an-1xn-1 + ... + a2x2 + a1x + a = 0

There may be several different values of x, called roots, that satisfy a univariate polynomial equation.  In general, the higher the order of the equation (that is, the larger the value of n), the more roots there are.

A univariate polynomial equation of degree 1 (n = 1) constitutes a linear equation.  When n = 2, it is a quadratic equation; when n = 3, it is a cubic equation; when n = 4, it is a quartic equation; when n = 5, it is a quintic equation.  The larger the value of n, the more difficult it is to find all the roots of a univariate polynomial equation.

Some polynomials have two, three, or more variables.  A two-variable polynomial is called bivariate; a three-variable polynomial is called trivariate.

This was last updated in May 2008

Join the conversation

3 comments

Send me notifications when other members comment.

By submitting you agree to receive email from TechTarget and its partners. If you reside outside of the United States, you consent to having your personal data transferred to and processed in the United States. Privacy

Please create a username to comment.

Because x^1 = x and x = 1 for all complex numbers x, ...

just guessing, maybe the right sentence is :

Because x^1 = x and x^0 = 1 for all complex numbers x, ...
Cancel
thank you for the answer
Cancel
very nice answer
Cancel

-ADS BY GOOGLE

File Extensions and File Formats

Powered by:

SearchCompliance

  • cyborg anthropologist

    A cyborg anthropologist is an individual who studies the interaction between humans and technology, observing how technology can ...

  • RegTech

    RegTech, or regulatory technology, is a term used to describe technology that is used to help streamline the process of ...

  • conduct risk

    Conduct risk is the prospect of financial loss to an organization that is caused by the actions of an organization's ...

SearchSecurity

  • application whitelisting

    Application whitelisting is the practice of identifying applications that have been deemed safe for execution and restricting all...

  • security

    Security, in information technology (IT), is the defense of digital information and IT assets against internal and external, ...

  • insider threat

    An insider threat is a malicious hacker (also called a cracker or a black hat) who is an employee or officer of a business, ...

SearchHealthIT

  • HIPAA Privacy Rule

    The Standards for Privacy of Individually Identifiable Health Information, commonly known as the HIPAA Privacy Rule, establishes ...

  • HIPAA business associate agreement (BAA)

    Under the U.S. Health Insurance Portability and Accountability Act of 1996, a HIPAA business associate agreement (BAA) is a ...

  • telemedicine

    Telemedicine is the remote delivery of healthcare services, such as health assessments or consultations, over the ...

SearchDisasterRecovery

  • data recovery

    Data recovery restores data that has been lost, accidentally deleted, corrupted or made inaccessible. Learn how data recovery ...

  • disaster recovery plan (DRP)

    A company's disaster recovery policy is enhanced with a documented DR plan that formulates strategies, and outlines preparation ...

  • fault-tolerant

    Systems with integrated fault tolerance are designed to withstand multiple hardware failures to ensure continuous availability.

SearchStorage

  • data deduplication

    Deduplication retains one unique data instance to reduce storage and bandwidth consumed by remote backups, replication and ...

  • byte

    In most computer systems, a byte is a unit of data that is eight binary digits long. Bytes are often used to represent a ...

  • Secure Digital card (SD card)

    SD cards use flash memory to provide nonvolatile storage. They are more rugged than traditional storage media and are used in ...

SearchSolidStateStorage

  • flash file system

    Flash file systems are designed specifically for memory devices. A well-designed flash device and flash file system ensure ...

  • IOPS (input/output operations per second)

    IOPS measures the maximum number of reads and writes to non-contiguous storage. It is not an actual benchmark since vendor ...

  • eMMC (embedded MultiMediaCard)

    An embedded MultiMediaCard (eMMC) is a small storage device made up of NAND flash memory and a simple storage controller.

SearchCloudStorage

  • RESTful API

    A RESTful application program interface breaks down a transaction to create a series of small modules, each of which addresses an...

  • cloud storage infrastructure

    Cloud storage infrastructure is the hardware and software framework that supports the computing requirements of a private or ...

  • Zadara VPSA and ZIOS

    Zadara Storage provides block, file or object storage with varying levels of compute and capacity through its ZIOS and VPSA ...

Close