Which expression is a polynomial in (x) if (m) is treated as a constant?

Correct answer: \(m^2x^3-5mx+6\)

Treating \(m\) as a constant, the powers of \(x\) in \(m^2x^3-5mx+6\) are 3, 1, and 0. All are non-negative integers, so it is a polynomial in \(x\). Option A has \(x^{-2}\), option B has \(\sqrt{x}=x^{1/2}\), and option C has \(\frac{m}{x}=mx^{-1}\); these powers are not permitted in a polynomial. Exam tip: For a polynomial in a given variable, every exponent of that variable must be a non-negative integer.