Question 840326: 3x^3 + 6x^2 - 3x - 6
Can someone help me solve this?
Answer by josh_jordan(263)   (Show Source):
You can put this solution on YOUR website! To solve this for x, you first need to perform the rational zero test, to determine all of the possible real zeros. Doing this will give you the following possible zeros:
+-1, +-2, +-3, +-6, +-1/3, +-2/3
Next you will have to test these possible zeroes by synthetic division. It's easier to start with the small integers first. If you start with 1, you will see that 1 IS a zero of this polynomial. Your remaining polynomial when you synthetically divide by 1, is
The first thing you can do is to factor out the 3 from that remaining polynomial, which will give you
Now, you can easily factor. Doing so, will give you
Set each of these factors equal to zero. You can remove the 3, because 3 = 0 is not a correct statement. Doing this will give you
x + 2 = 0 and x + 1 = 0
Solving for x in both of the above, will give you your other two zeros:
x = -2 and x = -1
Thus, the zeros for  are
-2, -1, 1
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