An easy way to avoid google remembering your previous searches and not to consider you G+ activity is to use the incognito mode.

This will then give you an idea about the SERP from a more neutral point of view, and a more correct idea of your own rankings.

How to use the incognito mode

It is actually very fast and simple. It can vary a bit depending on the browser you are using, but in general, you go to the setting and here you can choose incognito mode. In Chrome it is in the right hand corner (see picture below - hope it is not too confusing it is not in Danish, but think you get the idea).

Then a new black screen will come up (see picture below), and you can now do a search in incognito mode. An even faster way to open the incognito screen is on PC to press shift+ctrl+n (do not know the short cut on mac as I do not have one, but sure you can find it easily on google).

Next up, I will tell you what the incognito mode does not show you