Which of the following is a polynomial?

For option (a),

We have x – 1

Look at each term individually, there’s no violation of the definition of polynomials.

The exponent in the algebraic expression is non-negative integers, that’s why we can say that (x – 1) is a polynomial.

For option (b),

We have

Rearranging the expression, we get

Even after re-arranging the expression, notice that the variable in both terms is appearing in denominator, which does not satisfy the definition of polynomials as variables cannot appear in denominator in the expression of a polynomial.

For option (c),

We have

Simplifying the expression, we get

x² – 2x^-2 + 5

Look at the term 2x^-2.

In polynomials, the exponent in the algebraic expression should be non-negative integers, but in this expression the exponent is negative.

⇒ is not a polynomial.

For option (d),

We have

Simplifying the expression, we get

⇒

⇒

⇒

Observe the rational root in the second term of the expression, but in polynomials, the exponent should be non-negative integers.

⇒ is not a polynomial.

Thus, option (a) is correct.