Which expression is a polynomial in (x) with only odd powers and a constant term?

Correct answer: \(x^7-4x^5+2x-6\)

In option A, the variable terms have powers \(7, 5\), and \(1\), all of which are odd positive integers. The term \(-6\) is a constant, so \(x^7-4x^5+2x-6\) satisfies the condition. Option B includes the even power \(x^6\). Option C has the negative exponent in \(x^{-7}\), while option D has the fractional exponent \(\sqrt{x}=x^{1/2}\); therefore, neither is a polynomial in \(x\). Exam tip: Exponents of a variable in a polynomial must be non-negative integers.