Expert: Richard J. Raridon - 2/2/2011

Question
Can you show me the steps of factoring 54x^3=-2?

Answer
divide by 2 and re-write it to 27x^3+1 = 0
since 27 is a cube you know a factor has to start with 3x and it has to end with 1 so possible factors are 3x+1 and 3x-1, which means that x = +/-1/3.  If you try substituting those into the equation you will find that -1/3 is a solution so one of the factors is 3x+1.  
divide that into 27x^3+1 and the other factor is 9x^2-3x+1.