A polynomial is an algebraic expression in which all exponents of all variables should be zero and/or positive integer.
Going over thru each function we have the following
[tex]\begin{gathered} (a)\text{ }f(x)=5x(x-3)^2:\text{ YES} \\ \\ (b)\text{ }h(x)=-3\sqrt{x}:\text{ NO} \\ \text{Having a radical is the same as having a fraction as an exponent} \\ \\ (c)\text{ }u(x)=6x^{-4}+4x:\text{ NO} \\ \text{Negative exponent of the first term} \\ \\ (d)\text{ }v(x)=2-\frac{1}{x}:\text{ NO} \\ \text{Second term has an equivalent of a negative exponent }(-1). \end{gathered}[/tex]
