Question

State whether the following is a polynomial or not? Given reasons.
$\frac{1}{x}-1(x\ne 0)$

Answer 1

Given expression can be rewritten as,

$\frac{1}{x}-1=x^{-1}-1$

As we can observe that the exponent of variable $x$ is negative but for an expression to be a polynomial exponent of the variable must be whole numbers hence given expression is not a polynomial.