Given:
Given that there are 4 expressions.
We need to determine the expressions that are polynomials.
Option a: [tex]-7x^2+\frac{5}{3x}[/tex]
In the second term of the expression, the constant is divided by a variable.
For an expression to be a polynomial, it should not divided by a variable.
Hence, the expression [tex]-7x^2+\frac{5}{3x}[/tex] is not a polynomial.
Thus, Option a is not the correct answer.
Option b: [tex]-x^{2}+5 x[/tex]
The given expression satisfies the conditions of the polynomial.
Hence, the expression [tex]-x^{2}+5 x[/tex] is a polynomial.
Thus, Option b is the correct answer.
Option c: [tex]6 x^{2}+5 x[/tex]
The given expression satisfies the conditions of the polynomial.
Hence, the expression [tex]6 x^{2}+5 x[/tex] is a polynomial.
Thus, Option c is the correct answer.
Option d: [tex]x^{2}+5 x^{\frac{1}{5}}[/tex]
The second term of the expression contains the exponent [tex]\frac{1}{5}[/tex]
For an expression to be a polynomial, the fractional exponent is not allowed.
Hence, the given expression [tex]x^{2}+5 x^{\frac{1}{5}}[/tex] is not a polynomial.
Thus, Option d is not the correct answer.
