Which of the following is a polynomial: 

Concept -

A polynomial is a mathematical expression consisting of variables (also called indeterminates) and coefficients, combined using arithmetic operations like addition, subtraction, multiplication, and non-negative integer exponents. It's an expression made up of one or more terms, where each term comprises a constant coefficient multiplied by a variable raised to a non-negative integer exponent.

The general form of a polynomial is:

\(P(x) = a_nx^n + a_{n-1}x^{n-1} + \dots + a_1x + a_0 \)

Here:
-  P(x)  represents the polynomial in terms of variable  x.
- \( a_n, a_{n-1}, \dots, a_1, a_0 \) are constants known as coefficients.
-  x is the variable.
-  n is a non-negative integer representing the highest exponent (degree) in the polynomial.
- Each term of the polynomial consists of a coefficient multiplied by the variable raised to a non-negative integer exponent.

For example, \( 3x^2 + 2x - 5 \) and \( 4x^4 - 7x^3 + x^2 - 2x + 1\) are polynomials because they consist of terms where the variables have non-negative integer exponents and are combined using arithmetic operations.

(1) we have x2 + 3√x

Because of √x this is not polynomial.

(2) We have 2x2 + 3x

Clearly this is polynomial.

(3) We have \(\rm x^2+\frac{1}{x^2}-2\)

This is not follow the standard form of the polynomial.

(4)  We have 3x2 + 2√x

Because of √x this is not polynomial.

Hence the correct answer is 2x2 + 3x.