Question 306792
Use the factor theorem. List the factors of -18 and then plug them in to the function. If the function equals zero, then that means the number you chose is a factor.


Factors of -18: -1, 1, -2, 2, -3, 3, -6, 6, -9, 9, -18, 18


You know that your three factors will look something like this:


Choose a factor that is somewhere in the middle, like x=3, and plug it into the function.

x^3 +2x^2 -9x -18=0
3^3 +2(3^2)-9(3)-18 = 0


It's true! That means that (x-3) is one of the factors.


You can then use synthetic division to find the other two factors, or you can keep guessing and plugging in numbers. You know that (x-3) is a factor, so the other 2 factors have to multiply to +6 (because we know that the 3 factors multiply to -18).


A smart guess would be -2 or +2.


Try it, and you'll see that -2 works. That means that (x+2) is another factor. 


The third factor must be (x+3), in order to make the last term -18. You can check this by plugging x=-3 into the function. You will find that it is true.


So the factors are: (x-3)(x+2)(x+3)=0


Giving you roots of 3,-2,-3.


If you need any clarifications, let me know.