Yes. This can be programmed, but how to program really would depend on how you wanted to use it.
In the case that you want to extract all of the numbers at the beginning of each term, you can run:
eq = 3 x[1]^2 + 4 x[1] x[2]^(-1/2)
(List @@ eq)[[All, 1]]
The answer is basically that you will want to become familiar with pattern matching in order to do manipulations with algebra that aren't preprogrammed into Mathematica.
