Is the following expression a polynomial? Justify your answer:
$\frac{(x-2)(x-4)}{x}$

(N/A) First,expand the numerator: $(x-2)(x-4) = x^2 - 4x - 2x + 8 = x^2 - 6x + 8$.
Now,divide each term by $x$: $\frac{x^2 - 6x + 8}{x} = \frac{x^2}{x} - \frac{6x}{x} + \frac{8}{x} = x - 6 + 8x^{-1}$.
$A$ polynomial is an algebraic expression where the exponents of the variables must be non-negative integers (whole numbers).
In the expression $x - 6 + 8x^{-1}$,the third term $8x^{-1}$ has an exponent of $-1$,which is not a whole number.
Therefore,the given expression is not a polynomial.