When use As+B in partial fraction expansion
The choice depends on whether we want the constants to be real numbers or complex numbers.
A relevant portion from Wikipedia

If K is field of complex numbers, the fundamental theorem of algebra implies that all \$p_i\$ have degree one, and all numerators \$a_{i j}\$ are constants. When K is the field of real numbers, some of the \$p_i\$ may be quadratic, so, in the partial fraction decomposition, quotients of linear polynomials by powers of quadratic polynomials may also occur.

Example 2 shows an explicit example. They do the p.f.e both with real constants and complex constants.