Which statement is correct about \(x^2+\frac{x}{2}+9\)?

Correct answer: It is a polynomial of degree 2

Since \(\frac{x}{2}=\frac{1}{2}x\), the variable \(x\) is not in the denominator; \(\frac{1}{2}\) is only a coefficient. The terms are \(x^2\), \(\frac{1}{2}x\), and 9, whose exponents of \(x\) are 2, 1, and 0 respectively. All are non-negative integers, and the greatest exponent is 2, so it is a polynomial of degree 2. Option A wrongly treats the variable as being in the denominator, while option C looks at only one term instead of the whole polynomial. Exam tip: find the degree of a polynomial by identifying the greatest exponent of the variable among all its terms.