Which of the following expressions are polynomials in one variable and which are not? State the reason for your answer. If the given expression is a polynomial,state whether it is a polynomial in one variable or not: $5 x^{2}-7 x+3 \sqrt{x}$

(D) The given expression is $5 x^{2}-7 x+3 \sqrt{x}$.
To determine if an expression is a polynomial,the exponent of the variable must be a non-negative integer.
In the given expression,the term $3 \sqrt{x}$ can be written as $3 x^{\frac{1}{2}}$.
Here,the exponent of $x$ is $\frac{1}{2}$,which is not a non-negative integer.
Therefore,$5 x^{2}-7 x+3 \sqrt{x}$ is not a polynomial.