...At least this work with FF on my Win 8.1 machine; Open FF, click once on the little + sign in the search engine line in the upper right, which opens the search engine menu, (you can also change your default search engine here), then select "change search settings". At the next window will be a list of search engines which you can highlight and remove, if you'd like.
For Internet Explorer, (also on this Win 8.1 computer), open IE, click on "Tools-Manage Add-Ons-highlight "Search Providers" on the left. Once there, you can search for more search providers to add, make them default, then remove any you don't want.
Hope this helps.
Grif
I have IE, Firefox, and had Avant browsers installed....only used certain ones for specific websites because IE sometimes is really slow loading graphically intense sites.
Avant, two days ago, said a new version was available so I updated it....however, not only did it completely enlarge the pages with no 'fonts' option available to change that, but it also stopped the 'hand' from showing up to click links. I uninstalled it, rebooted the computer, and went to Chrome instead.
New issues have reared their ugly head now....NONE of browsers show the 'top sites' in new tabs anymore, and for Firefox and Chrome the homepage I set for it refuses to take. IE will flash the 'top sites' page in a new tab but it disappears quickly and a Yahoo search page shows up for all three instead (two as homepage) and a new tab for IE.
How do I put things back correctly? I've gone into the settings on all of them, and they show the original default settings that I want, but none take once the tab or program is closed and reopened. IE shows Bing as the default search engine, and Firefox and Chrome show Google as the default but none of them are what shows up and it's ticking me off because I can't find where to remove a search engine.

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