Divide $x^{2}+8x+12$ by $x+2$.

(A) Given dividend $p(x) = x^{2}+8x+12$ and divisor $s(x) = x+2$.
To divide $x^{2}+8x+12$ by $x+2$,we perform long division:
$1$. Divide the first term of the dividend $(x^{2})$ by the first term of the divisor $(x)$ to get $x$.
$2$. Multiply $x$ by $(x+2)$ to get $x^{2}+2x$.
$3$. Subtract $(x^{2}+2x)$ from $(x^{2}+8x+12)$ to get $6x+12$.
$4$. Divide the first term of the new polynomial $(6x)$ by the first term of the divisor $(x)$ to get $6$.
$5$. Multiply $6$ by $(x+2)$ to get $6x+12$.
$6$. Subtract $(6x+12)$ from $(6x+12)$ to get $0$.
Thus,the quotient is $x+6$ and the remainder is $0$.