Which expression is a polynomial in u, with x treated as a coefficient?

Correct answer: xu^3 - 4u + 2

When an expression is described as a polynomial in u, only the powers of u are checked. Any quantity independent of u may be treated as a coefficient, so x acts as a constant coefficient in this question. Option A, xu³ − 4u + 2, has u-powers 3, 1, and 0, all of which are non-negative integers. It is therefore a polynomial in u, even though its coefficient xu³ contains x. Option B has u in the denominator, giving u⁻¹. Option C has the negative exponent −2. Option D has √u = u^(1/2), a fractional exponent. Each of those violates the polynomial condition in u, so option A is the only valid choice.