Which of the following expressions is a polynomial

f(x)= -3x^4√x+13x^2-5x
f(x)=2/x^2-15x
f(x)=x^3-11x^2+3^x
f(x)=2x^3-5x^5-2/9x^2+9

f(x)=2x^3-5x^5-2/9x^2+9

Is the only one that is a polynomial

All expressions made with constants, variables, and exponents, which are combined using addition, subtraction and multiplication, and non-negative integer exponents.....but not division or roots... are defined as polynomials. So the answer is
x^3-11x^2 + 3^x
because the 1st expression -3x^(4sqrt x) + 13x^2-5x has a root involved in it. So ca'nt be a polynomial
the 2nd expression 2/x^2-15x involves a negative exponent because 2/x^2=2x^-2, so it, too, can't be a polynomial
3rd expression x^3-11x + 3^x is a polynomial
4th expression 2x^3-5x^2-2/9x^2 + 9 can't be a polynomial as 9/x^2=9x^-2

A polynomial can be defined as an algebraic expression with MORE than two algebraic terms. This means that the following is a polynomial:

f(x)= -3x^4√x+13x^2-5x

Remember, polynomials can only have exponents like 0, 1, 2, 3, etc. They cannot have a variable as an exponent. If they do, it isn't a polynomial.