Question

Question 1
Which one of the following is a polynomial?

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

Answer 1

The answer is C.
(a)
$\frac{x^2}{2}-\frac{2}{x^2}=\frac{x^2}{2}-2x^{-2}$, It is not a polynomial because exponent of x is - 2 which is not a whole number.

(b)
$\sqrt{2x}-1=\sqrt{2}{x}^{\frac{1}{2}}-1$, It is not a polynomial because exponent of x is $\frac{1}{2}$ which is not a whole number.

(c)
$x^2+\frac{3x^{\frac{3}{2}}}{\sqrt{x}}=x^2+3x^{\frac{3}{2}-\frac{1}{2}}=x^2+3x$, 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.