Answer: A polynomial is a mathematical expression that is composed of a sum of powers in one or more variables (indeterminates) with non-negative integer exponents, and coefficients that are real numbers.
Out of the options given, option "b" is not a polynomial.
Option "a" √3x^2-2√3x+3 is a polynomial, it consists of terms with non-negative integer exponents (x^2, x^1) and the coefficients are real numbers (√3, -2√3, 3)
Option "c" x+1/x is not a polynomial , it's called a rational function, it consists of one polynomial divided by another polynomial, it's not a polynomial because of the fraction 1/x
Option "d" 5x^2-3x+ √2 is a polynomial, it consists of terms with non-negative integer exponents (x^2, x^1) and the coefficients are real numbers (5, -3, √2)
So, option "b" 3x^3/2-5x^2-1/√2x-1 is not a polynomial, because of the fraction and the non-integer exponent (3/2)
Explanation: