Hello,
For you needs you several options:
-> With APM
-> With LTM Policy
-> With Irule (we can do It without Irule... but it's an option)
If you use APM you can create a macro and you can use landing URI (Initial URI) for each Pool...
And you can directly from VPE set pool depending the landing URI.
But after reflexion, you may have problems.
because once the policy evaluated you do not go back inside anymore.so if the user enters another URL he will not be redirected to the right pool but on the one selected during the evaluation of the policy...
So I advise you to use "LTM Policy" for your need.
It's simple to deploy and maintain...
Let me now if you have another question