I am looking for the definition of a polynomial.

### 7 Answers | Add Yours

**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 *a*0*x**n*+*a*1*x**n*-1+*a*2*x**n*-2+…+*a*n-1*x*+*an* where *n* is a positive integer and *a*0, *a*1, *a*2, … , *an* are any numbers. An example of a polynomial in one variable is 11*x*4-3*x*3+7*x*2+*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.

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:

- variables (like x)
- constants (like the 3 in 3x, or the 4 in x^2 + 2x + 4)
- 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.

[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

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

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.

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

Ex: 10x^2 + 5x - 9

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

For example; 3x^2-x+1

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes