What is the complete factorization 3x^2-75

After a first glance you can see that 3x^2 - 75 is not a difference of squares in the current form, because for one 3 and 75 are not squares. 

So we'll have to see if we can factor something out of both of them. The only number it can be is 3, because the only number besides 3 that goes into 3 is 1. 

So is there any number that can multiply by 3 to equal 75? 

If you said 25 then you are correct. :p 

So then our problem would look like this: 
3(x^2 - 25) 

Now we have a difference of squares!

Remember a difference of squares can be factored like this!

(a^2 - b^2) = (a - b)(a + b) 

3(x - 5)(x + 5)
Is our answer!