what exactly determines whether a video card will work with a motherboard and cpu?

is it simply the number of PCI express lanes that the CPU supports? for instance, the i7-3970x supports 40. but how many exactly does say, an nvidia/pny/hp/dell quadro fx 4000 video card use? 16?

http://www.nvidia.com/object/product-quadro-4000-u...

PCI Express 2.0 x16

how many lanes are used by the rest of the mobo on internal peripherals, if any?

or is the determining factor the GPU clock speed? or is it the gpu clock speed combined with the number of cores that you have to somehow match with either the cpu or cpu and mobo (specifically, what on the mobo?)?

is there something I am missing?