Question
Which of the following expression are polynomials$?$
$\frac{1}{\text{x}+1}$
$\frac{1}{\text{x}+1}$
✓
Answer
Not Polynomial, as the polynomial is expressed as $a_0+a_1 x+a_2 x+\ldots a_n x^n$,
where $a_0, a_1, a_{2, \ldots}, a_n$ are constants.
Now, $\mathrm{f}(\mathrm{x})=\frac{\mathrm{p}(\mathrm{x})}{\mathrm{q}(\mathrm{x})}$ is a rational expression where $\mathrm{q}(\mathrm{x}) \neq 0, \mathrm{p}(\mathrm{x})$ and $\mathrm{q}(\mathrm{x})$ are polyonimials.
Hence, $\frac{1}{x+1}$ is a rational expression but not a polyonimial.
where $a_0, a_1, a_{2, \ldots}, a_n$ are constants.
Now, $\mathrm{f}(\mathrm{x})=\frac{\mathrm{p}(\mathrm{x})}{\mathrm{q}(\mathrm{x})}$ is a rational expression where $\mathrm{q}(\mathrm{x}) \neq 0, \mathrm{p}(\mathrm{x})$ and $\mathrm{q}(\mathrm{x})$ are polyonimials.
Hence, $\frac{1}{x+1}$ is a rational expression but not a polyonimial.
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