SOLUTION: I'm having trouble with {{{9x^3-18x^2-4x+8=0}}} In my steps it says first to group the terms. I think that is where I may ultimately be messing up. I've worked on it for awhi

Algebra ->  Expressions-with-variables -> SOLUTION: I'm having trouble with {{{9x^3-18x^2-4x+8=0}}} In my steps it says first to group the terms. I think that is where I may ultimately be messing up. I've worked on it for awhi      Log On


   

Question 69073: I'm having trouble with
9x%5E3-18x%5E2-4x%2B8=0
In my steps it says first to group the terms. I think that is where I may ultimately be messing up. I've worked on it for awhile. The answers I am supposed to have when the problem is finished is: +2/3, -2/3, and 2
This pattern throws me off and I have more of them. A step by step guide would be a life saver.
~Jake
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You can use the technique of factoring by grouping to solve this problem.
9x%5E3+-+18x%5E2+-+4x+%2B+8+=+0 Group the terms as follows:
%289x%5E3+-+18x%5E2%29+-+%284x+-+8%29+=+0 Notice the change in sign of the last term. Factor 9x%5E2 from the first group and factor 4 from the second group:
9x%5E2%28x+-+2%29+-+4%28x+-+2%29+=+0 Now you can factor the common term (x - 2).
%28x+-+2%29%289x%5E2-4%29+=+0 Apply the zero product principle.
x-2%29+=+0 and/or 9x%5E2-4+=+0
If x-2+=+0 then x+=+2
If 9x%5E2-4+=+0 then 9x%5E2+=+4 and so x%5E2+=+4%2F9 and x+=+2%2F3 or x+=+-2%2F3
Solutions:
x+=+2
x+=+2%2F3
x+=+-2%2F3