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.
$x^{2} + x - 3 + \frac{4}{x}$

(D) The given expression is $x^{2} + x - 3 + \frac{4}{x}$.
We can rewrite the term $\frac{4}{x}$ as $4x^{-1}$.
Thus,the expression becomes $x^{2} + x - 3 + 4x^{-1}$.
$A$ polynomial is defined as an algebraic expression where the exponents of the variables are non-negative integers.
In this expression,the exponent of $x$ in the term $4x^{-1}$ is $-1$,which is a negative integer.
Therefore,the given expression is not a polynomial.