Which of the following expressions are polynomials? Which are not? Give reasons.
(i) $ 4 x^{2}+5 x-2 $
(ii) $ y^{2}-8 $
(iii) 5
(iv) $ 2 x^{2}+\frac{3}{x}-5 $

Given:

The given expressions are,

(i) \( 4 x^{2}+5 x-2 \)
(ii) \( y^{2}-8 \)
(iii) 5

(iv) \( 2 x^{2}+\frac{3}{x}-5 \)

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.

(i) $4x^2+5x-2$ is a polynomial. Here, the variables(x) in the terms are raised to a whole number power.

So, $4x^2+5x-2$ is a polynomial.

(ii) $y^2-8$ is a polynomial. Here, the variables(x) in the terms are raised to a whole number power.

So, $y^2-8$ is a polynomial.

(iii) $5$ can be written as $5x^0$. Here, the variables(x) in the terms are raised to a whole number power.

So, $5$ is a polynomial.

(iv) \( 2 x^{2}+\frac{3}{x}-5 \) can be written as $2x^2+3x^{-1}-5$. Here, the variable in the term is raised to the power $-1$ which is not a whole number.

Therefore, \( 2 x^{2}+\frac{3}{x}-5 \) is not a polynomial.