Find the quotient and remainder \[ \frac{x^{2}+9 x+22}{x+3} \text {. } \]

Step 1 ：Define the polynomial \(p1 = x^{2} + 9x + 22\) and \(p2 = x + 3\).

Step 2 ：Use the div function from the sympy library to find the quotient and remainder when \(p1\) is divided by \(p2\).

Step 3 ：The quotient and remainder are given by the output of the div function. The quotient is the first element of the output tuple and the remainder is the second element.

Step 4 ：\(\boxed{\text{Final Answer: The quotient is } x + 6 \text{ and the remainder is } 4}\). So, \(\frac{x^{2}+9 x+22}{x+3} = x + 6 + \frac{4}{x+3}\).