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

4 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
I was thinking the same! it's X to the power of 0 for sure.
Cancel
thank you for the answer
Cancel
very nice answer
Cancel

-ADS BY GOOGLE

File Extensions and File Formats

Powered by:

SearchCompliance

  • PCAOB (Public Company Accounting Oversight Board)

    The Public Company Accounting Oversight Board (PCAOB) is a Congressionally-established nonprofit that assesses audits of public ...

  • 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 ...

SearchSecurity

  • Advanced Encryption Standard (AES)

    The Advanced Encryption Standard, or AES, is a symmetric block cipher used by the U.S. government to protect classified ...

  • identity theft

    Identity theft, also known as identity fraud, is a crime in which an imposter obtains key pieces of personally identifiable ...

  • spear phishing

    Spear phishing is an email-spoofing attack that targets a specific organization or individual, seeking unauthorized access to ...

SearchHealthIT

SearchDisasterRecovery

  • call tree

    A call tree -- sometimes referred to as a phone tree -- is a telecommunications chain for notifying specific individuals of an ...

  • mass notification system (MNS)

    A mass notification system is a platform that sends one-way messages to inform employees and the public of an emergency.

  • disaster recovery as a service (DRaaS)

    One approach to a strong disaster recovery plan is DRaaS, where companies offload data replication and restoration ...

SearchStorage

  • CIFS (Common Internet File System)

    CIFS (Common Internet File System) is a protocol that gained popularity around the year 2000, as vendors worked to establish an ...

  • GlusterFS (Gluster File System)

    GlusterFS (Gluster File System) is an open source distributed file system that can scale out in building-block fashion to store ...

  • virtual memory

    Virtual memory is a memory management capability of an OS that allows a computer to compensate for physical memory shortages by ...

SearchSolidStateStorage

  • Tier 0

    Tier 0 (tier zero) is a level of data storage that is faster, and perhaps more expensive, than any other level in the storage ...

  • PCIe SSD (PCIe solid-state drive)

    A PCIe SSD (PCIe solid-state drive) is a high-speed expansion card that attaches a computer to its peripherals.

  • SSD caching

    SSD caching, also known as flash caching, is the temporary storage of data on NAND flash memory chips in a solid-state drive so ...

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