Front end shake

i drive a 2000 Oldsmobile Bravada.i just changed the outer tie-rod(passenger side),and there is still a fairly good shake coming from the front end.i have checked everything that comes to mind(true,not too sound a mind).my question is ,how would i check the steering gear box? thanks for your time.

Not sure why you suspect the steering box, but FYI the usual symptom associated with a worn steering box is excessive play in the steering wheel. Meaning you have would have to turn the wheel from say, 12 o’clock to 1 o’clock in order to begin turning right, and from 12 o’clock to 11 o’clock to begin turning left. Not saying your wrong, that’s my experience with a worn steering box.
But I’d take a hard look at the front tires, their wear and air pressure first. And if they are good, check the struts. If the vibration occurs only at certain speeds, especially around 60 mph, they might be the problem.

Did you check for a worn idler arm?

Tester