I have to figure out how x^3+216=0 is factored, and what potential solutions might be. I factored it like this: (x+3)(x+3)(x+24), resulting in the solutions being -3 (double route) and -24. But my book says these are not correct answers. Why not? Can you show me how to do it the right way? Thanks!

Question

I have to figure out how x^3+216=0 is factored, and what potential solutions might be.  I factored it like this: (x+3)(x+3)(x+24), resulting in the solutions being -3 (double route) and -24.  But my book says these are not correct answers.  Why not? Can you show me how to do it the right way? Thanks!

MathMate · Answer

Use A³+;B³=(A+B)(A²-AB+B²) A³-;B³=(A-B)(A²+AB+B²) and note that 216=6³