Which one of the following is a polynomial?

(A) $\frac{x^{2}}{2}-\frac{2}{x^{2}}$
(B) $\sqrt{2 x}-1$

(C) $ x^{2}+\frac{3 x^{\frac{3}{2}}}{\sqrt{x}}$


Given :

The given expressions are,


(A)  $\frac{x^{2}}{2}-\frac{2}{x^{2}}$


(B) $\sqrt{2 x}-1$


(C) $ x^{2}+\frac{3 x^{\frac{3}{2}}}{\sqrt{x}}$


To do :

We have to find which of the given expressions is polynomial.


Solution :


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


(A) $\frac{x^{2}}{2}-\frac{2}{x^{2}}$ is not a polynom[Math Processing Error]ial because the term $- \frac{2}{x^2}$ is equal to $-2x^{-2}$ and in this term the variable x is raised to the power $-2$ which is not a whole number.


So, $\frac{x^{2}}{2}-\frac{2}{x^{2}}$ is not a polynomial.


(B) $\sqrt{2 x}-1$ is not a polynomial, because the term $\sqrt{2x}$ is equal to $\sqrt{2} x^{\frac{1}{2}}$ which is not a whole number.


So, $\sqrt{2 x}-1$ is no a polynomial.


(C) $ x^{2}+\frac{3 x^{\frac{3}{2}}}{\sqrt{x}} = x^2 + 3 x^{\frac{3}{2} - \frac{1}{2}} = x^2 + 3x$. Here, the variables(x) in the terms are raised to a whole number power.


Therefore, option (C) $ x^{2}+\frac{3 x^{\frac{3}{2}}}{\sqrt{x}}$ is a polynomial. 

[Math Processing Errorial because the term √2x is equal to √2x1/2 and in this term the variable x is raised to the power 1/2

Updated on: 10-Oct-2022

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