How do you factor #8a^3+27#?
We can find one root immediately:
So factor out linear bracket
We know from the fact that this cubic expression has no quadratic or linear terms (and can hence be solved as above) that the other two of the three roots will be complex conjugate values (i.e.
We can see this also by considering the discriminant of the quadratic factor,
There is a rule to factor the sum of two cubes:
Just for completess, although you don't need it for this exercise, there is a similar formula for the difference of two cubes:
In your case,
Plus these values into the formula to get
Rewrite it as