Divide using long division. State the quotient, $q(x)$, and the remainder, $r(x)$. \[ \left(x^{3}+6 x^{2}+7 x+2\right) \div(x+1) \]

Step 1 ：We are given the polynomial \(x^{3}+6 x^{2}+7 x+2\) and we are asked to divide it by \(x+1\).

Step 2 ：We use polynomial long division to solve this problem. The process is similar to long division with numbers. We divide the highest degree term of the dividend by the highest degree term of the divisor to find the first term of the quotient. Then we multiply the divisor by this term and subtract the result from the dividend to find the remainder. We repeat this process until the degree of the remainder is less than the degree of the divisor. The quotient is the sum of the terms we found, and the remainder is the final remainder.

Step 3 ：After performing the division, we find that the quotient is \(x^{2}+5 x+2\) and the remainder is \(0\). This means that the original polynomial is exactly divisible by \(x+1\).

Step 4 ：Final Answer: The quotient, \(q(x)\), is \(x^{2}+5 x+2\) and the remainder, \(r(x)\), is \(0\). So, we have \(q(x) = \boxed{x^{2}+5 x+2}\) and \(r(x) = \boxed{0}\).