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Note: This was an answer to another post which had the same scenario but much less detail; I would have answered differently for this post, either way, hope this helps too.

Here's what you need to do.

• Boot from the bootable Ubuntu USB or CD.

• Select Install Ubuntu.

• Click Continue.


• Select the ”SOMETHING ELSE” option.

• Click Continue.


• The window below will appear. Select the partition (empty or without important data) wherein you want to install Ubuntu. In this example it is shown as free space, in your case, just select the partition you don't need or would like to put Ubuntu into. It doesn't matter if it is an NTFS partition because you can format it to another partition on the next screen. In the Device for boot loader installation, select your hard drive, not a partition.

• After selecting the partition, click on Change. In the “Use as” option select “Ext4 journaling file system” and select mount point as "/". Press OK.

• Click on "Install Now".


• 
  Reboot and you should see the grub menu prompting you to choose which OS you want to boot into. By default, the last OS installed (Ubuntu) will be the default OS. You can press Enter to boot into Ubuntu or use the up or down arrow to select another OS (windows) to boot.

The 4-partition limit no longer exists with disks that use the GUID Partition Table (GPT). GPT supports up to 128 partitions by default and does not include the concepts of primary, extended, or logical partitions (although many tools refer to all GPT partitions as "primary partitions," simply because those tools were written with the older MBR system in mind).

Intel-based Macs, the vast majority of computers that shipped with Windows 8, and some computers that shipped with Windows 7 (particularly beginning in mid-2011) all use GPT. Most PCs sold before mid-2011 use the older Master Boot Record (MBR) system, which is limited to four primary partitions, one of which may be an extended partition that can hold an arbitrary number of logical partitions. Thus, increasing numbers of readers of this question are likely to find that there is no problem; if the disk is partitioned using GPT, the 4-partition limit simply doesn't exist.

I had a HP netbook cq10 and I deleted Recovery and HP_tools without problems. I think HP_tools is required for updating the BIOS but you can always reinstall it onto to a thumb drive ( find the exe at HP.com). Recovery partition I deleted because there are ways of creating a bootable windows USB drive in Ubuntu.

Make a recovery disk - this should let you recover the original install if need be. Better yet, if you have the space, image the whole disk with clonezilla.

First, do NOT delete the first and second partitions - the first one is the boot partition, and the second is windows. I would recommend leaving the first partition completely alone

If you made a backup disk, it should have the same contents as the third partition. The 4th partition is likely used to boot the third partition. You should be able to remove both these partitions and reorganise the remaining partitions to your liking. I'd recommend a extended partition with logical volumes with the space for maximum flexibility - since you can have as many logical volumes as you want inside a extended partition.

You are thinking correctly I would say.

As you have the tools backup I would remove that partition and resize the sda2 partition. All I would do differently is do the resize in windows. Then leave the space as unallocated. Create your extended and logicals in ubuntu livecd.

Then boot the livecd/usb and install.

You can create the necessary partitions either with the installer - choose the Something Else option or use gparted - that is available on the livecd/usb (if you do that you still need to use the Something Else option os set the / and /home mountpoints)

Whatever you do end up doing - make sure you have backups - if you lose power during the shrinking of the partition you'll be glad.

I ran into this problem too.

HP TOOLS and RECOVERY have saved my computer from turning into a brick. Thanks to these partitions, after 6 years my HP Pavilion dm4 is still running fast and smooth. I strongly recommend keeping these.

Obviously SYSTEM and your NTFS partition has what you need for Windows so you can't get rid of those.

In the end, you really want to keep all 4!

So here's what I did to dual boot Ubuntu alongside Windows 7:

• Backup all my files from Windows.


• Figure out Windows recovery options in case of horrible failure (recovery DVD/recovery image...whatever you use to return to that fresh clean out-of-box state).


• Download Ubuntu 16.04 iso (so a couple years passed, but the problem persists right?) and put it in a bootable USB.


• Prepare to lose my Windows and all my files.


• Boot the USB with Ubuntu but just Try Ubuntu, don't install.


• Unmount partition drives (Click on the drive and choose unmount--otherwise GParted will yell at you).


• Open GParted Partitioner (type gpart... in the finder search).


• Delete my NTFS (C: or untitled) partition. It will become unallocated.


• Create a new Extended partition in the unallocated slot.


• Within the Extended partition, make a new Logical partition aligned to Cylinder instead of MiB and with file system NTFS. This will be my Windows partition. I made this 100GB and left 350GB free space following for Ubuntu.


• Make another Logical partition in the unallocated region following the NTFS I made, all within the Extended partition. Make this ext4 or whatever filesystem. This can be changed later but this will be where I can install Ubuntu after reinstalling Windows.


• Then hit the green check-mark and make these partitions. (If you messed up, just clear all or undo before hitting the check-mark.) Now I've effectively screwed up my Windows partition.


• Shutdown and start up my laptop and I see that Windows fails to load and startup repair keeps coming up. Since my HP TOOLS and RECOVERY are intact (which they should be) I can now perform a Minimized Recovery of Windows. This will install Windows into that NTFS partition within my Extended partition section. Do this and go get some coffee while my laptop reboots several times.


• Now that my have Windows again (yay!) I shut down and grab my bootable USB and install Ubuntu. This time, I can safely Install Alongside Windows into that remaining slot of the Extended partition--and mess around more with partitioning.

Best of luck,

washifu

Sad Edit: Factory Image Recovery or Minimized Image Recovery after having installed Ubuntu does not work well. I sadly lost both my SYSTEM and HP_TOOLS. However, System Restore seemed to work fine. In the end, since I lost HP_TOOLS, I just made that as my fourth primary partition. Technically RECOVERY is good enough...(weeps softly in a corner)

Pardon the brief answer here, I just wanted to say that I have just added a extended partition to my HP g7-1150us that had 4 primary partitions as others have described, without losing anything. Here is how:

Since the laptop is limited to 100Mbps network connection, I took the 640GB HD out of the laptop and connected to a SATA port on my linux PC for the process. You could just use the network connection and boot linux from CD on the laptop instead.

First, I made a full backup image file of the laptop HD using the dd command.

Then using gparted I shrank the windows OS partition to make room for the new extended partition I want to install.

Then I made image files of the individual partitions and the MBR also using dd. I noted the start sector positions of each partition as indicated in gparted.

Then using gparted, I deleted the small HP_TOOLS partition from the laptop HD.

Then I created an extended partition using all of the free space with gparted.

Then I moved the RESTORE partition into the extended partition as a new logical partition all the way to the right within the extended partition using gparted again.

Then I resized the extended partition until the starting sector of the RESTORE logical position was the same as before. I am not sure if this was required or not.

Then I created a fat32 primary partition at the same starting sector that the HP_TOOLS partition was at before I deleted it, using gparted. Again I am not sure if lining up the starting sector is required for this to work.

Then I used dd to copy the HP_TOOLS backup image into the newly created fat32 partition.

I put the HD back into the laptop, checking windows boot, tools boot (F2) and restore boot (F11). They all worked just fine. No need for USB or permanently deleting potentially useful factory installed partitions.

To summarize, I just moved the RESTORE partition into a new extended partition and everything works.

What remains to be seen, is how GRUB will work with all of this after I install Linux within the extended partition. I am almost certain that the HP_TOOLS and RESTORE functions will stop working, but at least they are on the disk if needed. Additionally, in a serious crisis, I have a full image of the factory HD. Gparted and dd are excellent free tools to use for all of this.

UPDATE: Using a graphical Windows BCDeditor from neosmart.net I made Windows in control of the option to boot Linux. When I installed Ubuntu 12.04 from a USB drive (I used unetbootin to create the USB image from the 12.04 ISO image) I am now able to boot Windows, use F2 for tools, use F11 for restore and boot into Ubuntu. So if anyone was wondering, yes, it is possible to install Linux alongside Windows 7 on a HP laptop that was factory installed with 4 primary partitions, without losing any of the factory functionality and without having to burn DVD's and without having to keep a USB drive around for emergencies.

Happy hacking and cheers!