Sorry, I don't know enough about Polaris skis, but on other skis you can shear the flywheel key and throw off the timing, which will cause the backfire or not start at all. Or it could be a problem with the voltage output from the stator. If that is the problem, you will have to pull the engine to check it. This problem is more rare than a problem with the carb(s), but very possible. If you have a service manual for your ski, it probably shows how to check the output voltage from the stator. That would tell you if that is the problem or not.
If its been a while since the carbs. were cleaned or rebuilt, I'd do that as a frist step. Backfiring can occur from both lean and too rich settings, and carb related problems causing changes in fuel flow are probably the biggest cause.
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2008 Yamaha FX HO Cruiser
2010 Hurricane Sundeck 2100
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