Why is this so cheap??

If the D3000 has a built-in AF motor then this lens will work... If it doesn't then it will still work but you'll have to focus it manually which, believe me, is a real pain with long zooms. The price probably reflects the above... I think the built-in AF version is only about £150 so that price makes sense. I note though that it's a third-party seller and not direct from Amazon so as always, buyer beware.
 
Because is just a cheap lens, and yes it will work with your D3000.
 
Nikon AF 70-300/4.0-5.6 G Black Nikkor Lens

It's pretty much this part and also the optics that result in the low price. There's another reason as well.....can't quite think what it could be..... ;)
 
(not compatible with D40/D40x/D60/D5000) or 3000
 
If you're looking for a cheap-ish 70-300mm which WILL autofocus on your camera then I recommend taking a look at THIS from Sigma... It's a great lens in good light and has the added benefit of a "macro" setting (not full 1:1 though) for close-up shooting.

I took this with my one the other week...

 
Aww, cute fox! I quite like foxes, shame my dog wants to tear them to pieces every night :(
 
Its a cheaply built lens - bought one once for a D50. Big mistake.
 
tbf for a few quid more you could get a 55-200mm VR - you'll lose 100mm zoom (but gain 15mm wide) and get VR, it's really sharp and really great, loved mine (only sold it to fund a 70-200mm 2.8)
 
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