Question

Which one of the following is a polynomial?

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

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

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

(4) $\frac{x-1}{x+1}$

Answer 1

(a) $\frac{x^2}{2}-\frac{2}{x^2}=\frac{x^2}{2}-2x^{-2}$

Exponent of x cannot be negative.
Therefore, it is not a polynomial.

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

Exponent of x must be a whole number.
Therefore, it is not a polynomial.

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

It is a polynomial.

(d) $\frac{x-1}{x+1}$

It is not a polynomial.


Hence, the correct option is (c).