Why do we need to include a repeated linear factor when using partial fraction integration?

example: 1/(x+2)^2 = a/(x+2) + b/(x+2)^2. Why can't we treat that "b" term as a quadratic with a "bx +c" in the numerator? I know we HAVE to do it this way but I haven't found a good explanation as to WHY.

Please help!

Bret