Which of the following expressions is a polynomial in the variable \(x\)?

Correct answer: \(4x^3-2x+7\)

In \(4x^3-2x+7\), the powers of \(x\) are \(3\), \(1\), and \(0\). All are non-negative integers, so it is a polynomial in \(x\). In option A, \(\frac{3}{x}=3x^{-1}\); option B has \(\sqrt{x}=x^{1/2}\); and option D has \(x^{-2}\). These contain negative or fractional powers, so they are not polynomials. Exam tip: in a polynomial, variable exponents can only be \(0,1,2,\ldots\).