Express
2x3+7x2+8x+2(x+1)(x+2)\displaystyle \frac{2x^3 + 7x^2 + 8x + 2}{(x + 1)(x + 2)}(x+1)(x+2)2x3+7x2+8x+2
in the form
Ax+B+Cx+1+Dx+2\displaystyle Ax + B + \frac{C}{x + 1} + \frac{D}{x + 2}Ax+B+x+1C+x+2D
where AAA, BBB, C C\,C and D D\,D are integers.