Your how. First go to your app tray and look for google settings.
Tap on that grey Google Settings icon and the following screen will appear.
Then select account history and you'll see the following screen.
Now tap Google search history but, not the pencil. You'll see the following screen.
Now since you want to edit the search history, you'll tap the green underlined link at the bottom which says existing search history, and it will take you to the following screen. See below.
Now to remove any items, it will take you to a browser window that shows your entire search history. You'll see check mark boxes to the left of each item that's been searched in the past, and the option to remove those items at the top so you will check the ones you want removed as you scroll down and when you're finished selecting, go back to the top and click Remove [selected] Items. See below.