It is rare for a camera lens to have a fault that would cause shots to
be out of focus as it is zoomed.  And Fuji have a fairly good
reputation for their optics.  It is, however, very common for people to
think they can use long telephoto shots without keeping the camera
*rock* steady - in general terms your shutter speeds should always be
at least as high as the 35mm-focal-length equivalent.  So, if you are
shooting at, say 200mm zoom (which would be about 2/3 of the way
towards the optical zoom limit of that camera), your shutter speed
should be at least 1/200 (or preferably quicker) to avoid camera shake
problems.  Bright daylit shots should be fairly easy, but anything less
may not.  Does increasing the ISO setting help?

Can you post some examples?  Do you know how to recognise the
difference between out-of-focus, and camera shake?  Camera shake has a
directionally 'smeared' effect that looks quite different to o-o-f.

Hence the question about the tripod!  And I still would be questioning
whether it is a camera steadiness problem, or maybe a
'not-giving-the-AF-enough-time' problem, as it may take longer to focus
at long focal lengths or under low-ish light conditions..  Lastly, if
you have eliminated all those, then back to the supplier I guess.
Sorry if you are aware of all of the above, but you haven't given all
that much info to go on.