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Dan
It is not clear what you are doing, but you should not
be going to www.google.com to enter your search terms
as you can start directly from Firefox and enhance your
search later if needed on a search results list from Google.
It kind of sound like you set your homepage to google.com
If you are doing your searches from the address bar
I would certainly recommend against that, Phishing
sites being one reason not to leave anything to chance.
http://www.mvps.org/dmcritchie/firefox/search.htm
There is the builtin FF search bar that you select Google
in the dropdown and it stays there set to Google for
later searching -- like Google is the original default
http://www.mvps.org/dmcritchie/firefox/rightff.htm#searchbar
You can create your own search engines as well
http://www.mvps.org/dmcritchie/firefox/searchengine.htm
There are keyword shortcuts in Firefox that you can
use. http://www.mvps.org/dmcritchie/firefox/kws.htm
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David McRitchie, Firefox customizations/extensions notes, see
http://www.mvps.org/dmcritchie/firefox/firefox.htm