I need help on how to factorise this 8x^3-27

Question

system of equation and more

Answer 1

8x^3 - 27 = 0 

8x^3 = (2x)^3 

(2x)^3 = 3^3 

2x = 3 --> 2x - 3 is a factor 

Divide by 2x - 3 

(8x^3 - 27)/(2x - 3) = 4x^2 + 6x + 9 

Now solve for 0 and factor 

4x^2 + 6x + 9 = 0 

x = [-6 +/- sqrt(-108)]/8 

x = (3/4)(-1 +/- i√3] 

So the solutions are: 

x = 3/2 
x = -(3/4)(1 + i√3) 
x = -(3/4)(1 - i√3