Find the quotient and remainder using long division for: $\frac{x^{2}+7 x+17}{x+3}$. The quotient is The remainder is

Step 1 ：We are given the problem to find the quotient and remainder using long division for: \(\frac{x^{2}+7 x+17}{x+3}\).

Step 2 ：We perform polynomial long division to find the quotient and remainder. The process is similar to long division of numbers. We divide the highest degree term of the numerator by the highest degree term of the divisor to find the first term of the quotient.

Step 3 ：Then we multiply the divisor by this term and subtract the result from the numerator to find the remainder.

Step 4 ：We repeat this process until the degree of the remainder is less than the degree of the divisor.

Step 5 ：Finally, we find that the quotient is \(x+4\) and the remainder is \(5\).

Step 6 ：So, \(\frac{x^{2}+7 x+17}{x+3} = x+4 + \frac{5}{x+3}\).

Step 7 ：\(\boxed{\text{The quotient is } x+4 \text{ and the remainder is } 5}\)