The following expressions are polynomials? Justify your answer:
$\frac{(x-2)(x-4)}{x}$
The following expressions are polynomials? Justify your answer:
$\frac{(x-2)(x-4)}{x}$
$\frac{(x-2)(x-4)}{x}=\frac{x^{2}-6 x+8}{x}=x-6+\frac{8}{x}=x-6+8 x^{-1}$
Here, the exponent of variable $x$ in the third term, i.e., in $8 x^{-1},$ is $-1,$ which is not a whole number.
So, this algebraic expression is not a polynomial.
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