Question

If $x^9+\frac{1}{x^a}$ is a polynomial in one variable, What could be the value of $a$?

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

Answer 1

The correct option is B

any positive integer

For an expression to be a polynomial, the exponents of $x$ should be whole numbers. The above expression can be written as $x^9+x^{-a}$ For this to be a polynomial, $-a$ should be a whole number. This is possible if $a$ is a non-positive integer.