Sub internal amp

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I have a 2 ch Yamaha 100wpc integrated amp that does not have a line out or sub out connection. I am looking to h.u. a sub woofer to my second set of speaker level outputs. Do I still need a powered sub? My other speaker outs feed Polk rti8 speakers (with minimal bass). I plan to not power the rti8's via the out connectors on the sub. My room is 3600 cu ft and I am looking to use the Polk xt12 sub that utilizes an AB amp as does my main amp. Is there another sub available that doesn't have an internal amp that would be adequate? Note that I don't plan to run system at very high volume.

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