Which expression is a polynomial in (x) while (y) is treated as a coefficient?

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

With respect to \(x\), \(y\) is treated as a coefficient. In option A, the powers of \(x\) are \(3,1\), and \(0\), all of which are non-negative integers. Therefore, \(y^2x^3-2yx+5\) is a polynomial in \(x\). In option B, \(x\) is in the denominator, so its exponent is \(-1\); in C, the exponent of \(x\) is \(\frac12\); and in D, it is \(-2\). Hence, these are not polynomials in \(x\). Exam tip: check exponents only of the variable in question; they must be \(0,1,2,\ldots\).