Answer:
The following expressions are polynomials:



The following expressions are not polynomials:


![\sqrt[4]{x}-\sqrt[3]{x}+4\sqrt{x}-8x+16](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7Bx%7D-%5Csqrt%5B3%5D%7Bx%7D%2B4%5Csqrt%7Bx%7D-8x%2B16)
Step-by-step explanation:
We are required to differentiate the expressions as polynomials and non-polynomials.
Since, we know,
A polynomial is an expression that involves variables and their coefficients separated by mathematical operations with the variables having non-negative integer values.
i.e. A polynomial is of the form,
, with 'n' being non-negative integer.
Thus, according to the definition, we have that,
The following expressions are polynomials:



The following expressions are not polynomials:


![\sqrt[4]{x}-\sqrt[3]{x}+4\sqrt{x}-8x+16](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7Bx%7D-%5Csqrt%5B3%5D%7Bx%7D%2B4%5Csqrt%7Bx%7D-8x%2B16)