Question 306792: I seem to be having a lot of trouble with this problem on my algebra lesson and was wondering if I could get some help? I need to solve for x.
x^3 + 2x^2 - 9x = 18
Any help that could be given would be much appreciated, thanks.
Bre
Found 2 solutions by texttutoring, papas101280:
Answer by texttutoring(324)   (Show Source):
You can put this solution on YOUR website! 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.
Answer by papas101280(2)  (Show Source):
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