Which one of the following is a polynomial?

MCQ

Which one of the following is a polynomial$?$

A
$\frac{\text{x}^2}{2}-\frac{2}{\text{x}^2}$
B
$\sqrt{2\text{x}}-1$
C
$\text{x}^2+\frac{3\text{x}^{\frac{3}{2}}}{\sqrt{\text{x}}}$
✓
$\frac{\text{x}-1}{\text{x}+1}$

✓

Answer

Correct option: D.

$\frac{\text{x}-1}{\text{x}+1}$

The answer is $C.$
$(a)$
$\frac{x^2}{2}-\frac{2}{x^2}=\frac{x^2}{2}-2 x^{-2}$, It is not a polynomial because exponent of $x$ is $-2$ which is not a whole number.
$(b)$
$\sqrt{2 x}-1=\sqrt{2} x^{\frac{1}{2}}-1$, It is not a polynomial because exponent of $x$ is $\frac{1}{2}$ which is not a whole number.
$(c)$
$x^2+\frac{3 x^{\frac{3}{2}}}{\sqrt{x}}=x^2+3 x^{\frac{3}{2}} \frac{1}{2}=x^2+3 x$, it is a polynomial because exponents of $x$ are whole numbers.
$(d)$
$\frac{x-1}{x+1}$ it is not a polynomial because it is a rational function.

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