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I am looking for the definition of a polynomial.

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j1000 | High School Teacher | eNotes Newbie

Posted December 17, 2008 at 2:27 AM via web

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I am looking for the definition of a polynomial.

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torander | Student, Undergraduate | eNotes Newbie

Posted December 17, 2008 at 2:37 AM (Answer #1)

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Polynomial, mathematical expression which is a finite sum, each term being a constant times a product of one or more variables raised to powers. With only one variable the general form of a polynomial is a0xn+a1xn-1+a2xn-2+…+an-1x+an where n is a positive integer and a0, a1, a2, … , an are any numbers. An example of a polynomial in one variable is 11x4-3x3+7x2+x-8. The degree of a polynomial in one variable is the highest power of the variable appearing with a nonzero coefficient; in the example given above, the degree is 4.

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cburr | Middle School Teacher | (Level 2) Associate Educator

Posted December 17, 2008 at 8:26 AM (Answer #2)

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In case you had trouble understanding those two complex definitions, here's a simpler one.

First, poly means many, and nomial means name.  So, a polynomial has more than one part to it.  

It is a mathematical expression -- in other words, a string of mathematical symbols that aren't nonsense.

There are three kinds of things that can be in a polynomial:

  1. variables (like x)
  2. constants (like the 3 in 3x, or the 4 in x^2 + 2x + 4)
  3. whole number exponents that aren't negative (like x^2, but not x^-2 or x^1/4)

Lastly, the expression can have addition, subtraction and multiplication, but not division.

I hope this is helpful. 

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lulu-pixy | Student, Undergraduate | (Level 2) eNoter

Posted December 17, 2008 at 2:53 AM (Answer #3)

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[poly–, + (bi)nomial.] (adjective) Of, relating to, or consisting of more than two names or terms. (noun) A taxonomic designation consisting of more than two terms. Mathematics An algebraic expression consisting of one or more summed terms, each term consisting of a constant multiplier and one or more variables raised to integral powers. For example, x 2 − 5 x + 6 and 2 p 3 q + y are polynomials. Also called multinomial An expression of two or more terms

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dracomath | Student, Grade 11 | (Level 1) Honors

Posted December 28, 2008 at 12:38 AM (Answer #4)

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 A polynomial is an expression containing more than a term.  (ex: x²+2x+1)

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revolution | College Teacher | (Level 1) Valedictorian

Posted July 17, 2010 at 10:33 PM (Answer #5)

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Polynomial is a maths expression that has a finite sum and consists of variables and constants and also other operations like addition, subtraction, multiplication and division.

Its exponent must also be a positive number and also a whole number, not a negative number or a fractional index. x^2+2x+3 is a polynomial and not X^3/2+ X^(-2)+2x-3.

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atyourservice | Student, Grade 10 | (Level 3) Valedictorian

Posted April 19, 2014 at 9:48 PM (Answer #6)

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 A polynomial is a math expression with variables and more than 1 term.

Ex: 10x^2 + 5x - 9

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zumba96 | Student, Grade 11 | (Level 2) Valedictorian

Posted May 9, 2014 at 11:40 PM (Answer #7)

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It is a math term that includes variables with more than 2 algebraic terms. 

For example; 3x^2-x+1

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