Which expression is a polynomial with only odd powers and a constant term?

Correct answer: \(x^5-2x^3+x-9\)

In \(x^5-2x^3+x-9\), the powers of \(x\) are 5, 3, and 1, all odd positive integers, and \(-9\) is the constant term. Therefore, it satisfies both conditions in the question. \(x^4+x^2+1\) is a polynomial, but its variable terms have even powers. \(x^{-3}+x\) has a negative exponent, while \(\sqrt{x}+x^3\) contains \(x^{\frac12}\); hence neither is a polynomial. Exam tip: exponents of variables in a polynomial must be 0 or positive integers.