How do I factor out 12x^2+15?

Question

I just want to double check on how it's properly done

Answer 1

12 X² + 15 = 3 ( X² + 5 )  = 3 ( X + i √5 ) ( X - i √5 )

 

            This is factor into complex number  , where i² = -1 

Answer 2

It is prime in real domain.

In complex domain,

12x^2+15 = 12(x^2 + 5/4) = 12[x+i*sqrt(5)/2][x-i*sqrt(5)/2]