Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer:$ x-\frac{4}{x} $

Given:

The given expression is \( x-\frac{4}{x} \).

To do:

We have to find whether the given expression is a polynomial in one variable.

Solution:

Polynomials:

Polynomials are expressions in which each term is a constant multiplied by a variable raised to a whole number power.

\( x-\frac{4}{x} \) can be written as $x-4x^{-1}$. Here, the variable in the term $-4x^{-1}$ is raised to the power $-1$ which is not a whole number.

Therefore, \( x-\frac{4}{x} \) is not a polynomial.   

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Updated on: 10-Oct-2022

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