The easiest way to remove all traces of these files is to write over the portions of your drive with either zeros or with a randomly generated file. There are other methods like dban which is likely your best bet but most times it takes far too long (unless you are really paranoid).
I tend to use an Ubuntu Live CD and use the following commands to either write zeros or randoms to erase my disc.
sudo dd if=/dev/zero of=/dev/sda bs=1M
Note: if you would just like to create a large empty file with this command you can add count=
Just replace /dev/zero with /dev/random as follows:
sudo dd if=/dev/random of=/dev/sda bs=1M
That's about it!