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

SearchCompliance

SearchSecurity

  • copyright

    Copyright is a legal term describing ownership of control of the rights to the use and distribution of certain works of creative ...

  • keylogger (keystroke logger or system monitor)

    A keylogger, sometimes called a keystroke logger or system monitor, is a type of surveillance technology used to monitor and ...

  • password

    A password is an unspaced sequence of characters used to determine that a computer user requesting access to a computer system is...

SearchHealthIT

SearchDisasterRecovery

  • business continuity plan (BCP)

    A business continuity plan (BCP) is a document that consists of the critical information an organization needs to continue ...

  • 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.

SearchStorage

  • CompactFlash card (CF card)

    A CompactFlash card (CF card) is a memory card format developed by SanDisk in 1994 that uses flash memory technology to store ...

  • email archiving

    Email archiving (also spelled e-mail archiving) is a systematic approach to saving and protecting the data contained in email ...

  • RAID (redundant array of independent disks)

    RAID (redundant array of independent disks) is a way of storing the same data in different places on multiple hard disks to ...

SearchSolidStateStorage

  • M.2 SSD

    An M.2 SSD is a solid-state drive (SSD) that conforms to a computer industry specification written for internally mounted storage...

  • NVMe (non-volatile memory express)

    NVMe (non-volatile memory express) is a host controller interface and storage protocol to enable a solid-state drive to use the ...

  • SSD RAID (solid-state drive RAID)

    SSD RAID (solid-state drive RAID) is a methodology commonly used to protect data by distributing redundant data blocks across ...

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