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How to determine whether a function is a polynomial or not?

Question:

How to determine whether a function is a polynomial or not?

Polynomial:

  • An expression containing only one term in which powers of variables are non-negative integers is called a monomial.
  • An expression containing one or more terms is called a polynomial.

Answer and Explanation:

A polynomial function in {eq}x {/eq} is of the form:

$$f(x)=a_{n} x^{n}+a_{n-1} x^{a-1}+a_{n-2} x^{n-2}+\cdots+a_{2} x^{2}+a_{n} x+a_{0} $$

Here, {eq}a_{n} ,a_{n-1} , a_{n-2} ,\cdots,a_{2} x^{2},a_{n} x, \text{ and }a_{0} {/eq} are constants and {eq}n {/eq} is always a whole number.


For example:

{eq}x^2+3x + 5 {/eq} is a polynomial as all the exponents are whole numbers.

{eq}x^{-2} + 3x+5 {/eq} is NOT a polynomial as one of the exponents is negative (not a whole number).


Learn more about this topic:

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What Are Monomials & Polynomials?

from 6th-8th Grade Math: Practice & Review

Chapter 55 / Lesson 1
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