Yes, and no.
Pretty clear huh? lol!
Let me explain a few rudimentary things first. May be a long read, and a 'bumpy ride'.
Laptop manufacturers tend to 'exaggerate', in order to sell laptops.
They can get away with this due to their 'advertising license'.
"This laptop has an XXXXXX graphics card"
When in reality it isn't a graphics card. It is a graphics chipset soldered directly to the motherboard.
The term 'graphics card' is used rather loosely.
A graphics card is actually a graphics adapter card.
The graphics chipset is soldered to a circuit board, or 'card'.
The circuit board has contact pins on it, which plug into a connector on the motherboard.
This is a basic example for a desktop computer,http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=7168071
A graphics card made by Powercolor, and uses the AMD ATI Radeon HD5450 graphics chipset.
Left-click on the photo of the graphics card shown at the top.
It will come up in a separate window.
In the views at the Bottom, click on the second view from the left.
Here you will see the gold plated contact pins.
To show the gold plated contact pins in more depth, let's look at an average SO-DIMM ram memory module, for a laptop,http://en.wikipedia.org/wiki/File:1GB_DDR2_SO-DIMM.png
[ You can click on the photo to enlarge. You can enlarge twice ]
These gold plated contact pins go down into a slot. A graphics card slot. (Expansion slot on the motherboard)
For laptops that TRULY do use a graphics adapter card, they use the MXM technology. There IS a graphics adapter card, and it DOES plug into the motherboard.
This is an example of an ATI Radeon HD5450 MOBILE graphics card, that uses the MXM technology,
(Mobile meaning for a laptop. Laptops are a Mobile computer. Can take it with you wherever you go),http://www.ebay.com/itm/HP-ATI-Mobility-Radeon-HD-5450-MXM-Type-A-Graphics-Card-512MB-DDR3-608544-001-/190626056695?pt=UK_Computing_Computer_Components_Graphics_Video_TV_Cards_TW&hash=item2c6232c9f7
Here you see the gold plated contact pins again. Means this mobile graphics card, (Mobile meaning laptop), plugs into the laptop's motherboard.
It is mounted to the laptop's motherboard, with screws through those brass ringed holes you see. (Probably with just two holes)
MOST laptops do not use a graphics adapter card, based on the MXM technology.
They just have a graphics chipset soldered directly to the motherboard.
Let's regress for a moment, and let me explain Chipset, GPU, and BGA surface mount.
Chip and Chipset are slang terms for I.C.
[ A Processor is just ONE example of an Integrated Circuit ]
G.P.U. stands for Graphics Processing Unit,
The chipset, or Integrated Circuit, for graphics, is a GPU,http://en.wikipedia.org/wiki/GPU
Left-click on the photo to the upper right, that the heading states,
GeForce 6600GT (NV43) GPU
The actual GPU (Goldish/brown square), is in the center of that square
green circuit board. The GPU uses the green circuit board, to connect to the motherboard.
The entire thing you see is termed as the graphics chipset, or GPU.
This is because that circuit board is actually part of it.
BGA surface mount:
Ball Grid Array,http://en.wikipedia.org/wiki/Ball_grid_array
To explain a BGA surface mount;
Compare to an older Intel Pentium 4 processor, that uses a Socket 478 processor socket,http://en.wikipedia.org/wiki/Socket_478
This particular processor socket has 478 socket holes.
The bottom of the Intel Pentium 4 processor, has 478 contact pins sticking out of the bottom.
With a BGA surface mount there are No contact pins on the chipset, (GPU in this case), nor are there socket holes.
The bottom of the graphics chipset has Solder Balls.
The motherboard area where it mounts, has matching Copper Pads.
(The copper pads have a gold plating on them)
The graphics chipset is set into place, over the matching copper pads on the motherboard, and then heat is applied.
Heat is applied at a specific temperature, and length of time.
This action melts the solder balls, which in turn solders the graphics chipset TO the copper pads.
[ Which in turn of course, solders the graphics chipset TO the motherboard ]
IF, you have a graphics chipset, THAT uses the MXM technology, and IS an actual graphics adapter card, you MAY be able to upgrade it.
IF, the graphics chipset is Integrated Graphics, and therefore uses the BGA surface mount, I would forget about it.
Replacing means using a BGA Rework Machine.
However things get more complicated, than just replacing a graphics chipset, that uses the MXM technology.
It isn't, " OH, it's a graphics card? I'll just take it out, and use a better graphics card."
Depends on what the motherboard chipset is, and what type of graphics interface it uses. PCI, or AGP, or PCI-Express.
(PCI, and AGP, and PCI-Express, are technologies. Doesn't just refer to the type of expansion slot )
Let's look at the specifications, for the Gateway NV59C41u Notebook PC,...(Continued in an additional Comment)