Question

If $x^g+\frac{1}{x^a}$ is a polynomial in one variable, what could be the value of ${}^{\prime }{a}^{\prime }$?

• A. only 1
• B. any positive integer
• C. any negative integer
• D. any integer

Answer 1

The correct option is C

any negative integer

For an expression to be a polynomial, the exponents of $x$ should be whole numbers. The above expression can be written as $x^g+x^{-a}$ For this to be a polynomial, $-a$ should be a whole number. This is possible if $a$ is a non-positive integer.