What is a polynomial function?

timer Asked: Nov 13th, 2015
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Question Description

when can an expression be considered NOT a polynomial? 

how do you determine the degree of a term? degree of a polynomial?

Tutor Answer

School: New York University

Thank you for the opportunity to help you with your question!

A polynomial is an expression which consists of variables, constants  and exponents joined using addition, multiplication, and subtraction. Example: 

x^2 + 5*x + 9 is a polynomial 

By the definition, both linear and quadratic functions can be considered polynomials.

When we have negative or fractions for exponents, or letters under a radical, an expression cannot be considered as a polynomial. Example

1/(X-1) + 6*X^2 is not a polynominal

Consider the polynomial: 

X^4 + 9X^3 - 2X^2 + 2

The degree of a polyniminal is the highest exponent so in above polynomial, the degree of the polynomial is 4.

The degree of the term is the exponent to which the variable in the term is raised. In the example above there are four terms of degree 4, 3, 2 and 0 (the constant term has degree 0). 

Please let me know if you need any clarification. I'm always happy to answer your questions.

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