Factor the polynomial completely

Question

Factor the polynomial completely

9n^2+4

Answer 1

I agree with Mark M. 

The only way to factor this polynomial would be to use imaginary (i) number values with FOIL-type factoring.

9n² + 4 = (3n + 2i)(3n - 2i)  

 

with knowledge and use of the imaginary numbers' chart, in which:

i  =  i 

i²  =  - 1   

i³  =  - i    

i⁴  =  - (i²)  =  - (- 1)  =  1  

 

and where i⁵  =  i ,  i⁶  =  i²  =  -1 , etc. in a repeating pattern for use with higher order exponents.