Answer:
The third and fourth options are the polynomials.
Explanation:
Part 1
In the expression:
[tex]\frac{y^2+3x^{\frac{1}{3}}}{4}[/tex]All the exponents in the algebraic expression must be non-negative integers in order for the algebraic expression to be a polynomial. Since the exponent of x is 1/3, it is not a polynomial.
Part 2
Given:
[tex]\frac{7x^2+8}{4x}[/tex]If there are variables in the denominator of the fraction, the expression cannot be a polynomial.
Part 3 and 4
The third and fourth expressions are polynomials in 2 variables (x and y).
The third and fourth options are the polynomials.