Which expression is a trinomial polynomial in (x)?

Correct answer: (2x^2-3x+9)

A trinomial is an algebraic expression with exactly three unlike terms. For it to be a polynomial in \(x\), the powers of \(x\) must be non-negative integers. In option B, \(2x^2-3x+9\), the three terms are \(2x^2\), \(-3x\), and \(+9\). Their powers are 2, 1, and 0, so all are allowed in a polynomial.

Option A has only two terms, so it is a binomial. Option C has only one term, so it is a monomial. Option D contains \(\sqrt{x}=x^{1/2}\), which has a fractional power and therefore is not a polynomial in x. Thus option B is the only expression that is both a polynomial in x and a trinomial. The supplied answer and explanation are correct.