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### What is a Polynomial? The Elements of Polynomials

### Sasha S says

A polynomial is a mathematical function of finite length composed of a series of variables (such as x, x^2, x^3 etc) and exponents formed by positive integers (whole numbers) with constant coefficients (the number before each variable).

They are hence all of the form:

fx^n + ex^n-1...dx^3 + cx^2 + bx + a

where a,b,c,d,e,f are all whole numbers and n (the highest power of x in the polynomial) is the order of the expression - or 'degree'

Sorry if some of the explanations seem condescending - I have no idea how much maths lingo ya know! hope it helps!

### Ronnie Lorenzo Mckinney Jr says

In Mathematics, a polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication and non-negative integer exponents. As an example of polynomial of a single indeterminate, is, which is a Quardratic polynomial.

### soumabha says

Polynomials are algebraic expressions that include real numbers and variables. Division and square roots cannot be involved in the variables. The variables can only include addition, subtraction and multiplication.

Polynomials contain more than one term. Polynomials are the sums of monomials.

A monomial has one term: 5y or -8x2 or 3.

A binomial has two terms: -3x2 2, or 9y - 2y2

The degree of the term is the exponent of the variable: 3x2 has a degree of 2.

When the variable does not have an exponent - always understand that there's a '1' e.g., 1x

8x2 3x -2 Polynomial

8x-3 7y -2 NOT a Polynomial The exponent is negative.

9x2 8x -2/3 NOT a Polynomial Cannot have division.

7xy Monomial