which of the following is a polynomial

A polynomial is an algebraic expression in which:

• Variables have only non‑negative integer exponents.

• There is no variable in the denominator and no roots of variables (no x\sqrt{x}x​, no x−1x^{-1}x−1, etc.).

• Terms are combined only by addition, subtraction and multiplication (no division by a variable).

So, in a typical MCQ with options like

• x22−2x2\dfrac{x^{2}}{2}-\dfrac{2}{x^{2}}2x2​−x22​
• 2x−1\sqrt{2x}-12x​−1
• x2+3x+5x^{2}+3x+5x2+3x+5
• x−1x+1\dfrac{x-1}{x+1}x+1x−1​

the expressions that are polynomials are exactly those where every exponent of xxx is a whole number and xxx never appears in a denominator or under a root, for example x2+3x+5x^{2}+3x+5x2+3x+5.

If you share the exact answer choices you have, I can point out which of the following is a polynomial step by step for each option.

Information gathered from public forums or data available on the internet and portrayed here.