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[edit] Before Firefox 1.5

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Firefox writes search engine files to /opt/mozilla/lib/firefox/searchplugins, which is, by default, readable only by root. This means users cannot add search engines. You can either chmod o+w this folder, or run firefox as root when you want to install a search engine.

To remove search engines, remove the appropriate search engine files in /opt/mozilla/lib/firefox/searchplugins. Next time you start Firefox the engine won't be in the list.

[edit] Since Firefox 1.5

Search engines could now be added in the user's profile. If you want to get a look : ~/.mozilla/firefox/xxx.default/searchplugins where xxx is you profile id).

[edit] Plugin Method

There is also a plugin for Firefox which makes this very easy. It is called OpenSearchFox. Once installed, to add a search engine just right click on the search field and follow the wizard.