Rewrite this expression as a mixed number and then select your answer from the choices. \[ \frac{3 x^{2}+5 x-15}{x-2} \]

To rewrite the expression \(\frac{3x^{2}+5x-15}{x-2}\) as a mixed number, we can start with polynomial long division. Dividing \(3x^2 + 5x - 15\) by \(x - 2\): 1. Divide the first term: \(\frac{3x^2}{x} = 3x\). 2. Multiply: \(3x(x - 2) = 3x^2 - 6x\). 3. Subtract: \((3x^2 + 5x - 15) - (3x^2 - 6x) = 11x - 15\). 4. Now, divide \(11x\) by \(x\) to get \(11\). 5. Multiply: \(11(x - 2) = 11x - 22\). 6. Subtract: \((11x - 15) - (11x - 22) = 7\). Now we have a quotient of \(3x + 11\) and a remainder of \(7\). Thus, we can express it as: \[ 3x + 11 + \frac{7}{x - 2} \] So, the mixed number form of the expression is \(3x + 11\) with a remainder of \(\frac{7}{x-2}\).