Which of the followings is a polynomial in one variable?

Let us check for the option (a),

We have

We can write it as, x + 2x^-1 + 3.

Here, x^-1 is a polynomial.

⇒ x + 2x^-1 + 3 is not a polynomial.

⇒ is not a polynomial.

For option (b),

We have

We can write it as, 3√x + 2x^-1/2 + 5.

Here, x^{- 1/2} is not a polynomial.

⇒ 3√x + 2x^{- 1/2} + 5 is not a polynomial.

⇒ is not a polynomial.

For option (c),

We have √2x² - √3x + 6

Term-wise, √2 x² is a polynomial

√3 x is a polynomial

6 is a polynomial

⇒ √2 x² - √3 x + 6 is a polynomial.

For option (d),

We have x¹⁰ + y⁵ + 8.

Here, we have two variables, x and y.

Hence, it is clearly not a polynomial of single variable.

Thus, option (d) is correct.