posted by Momo .
One solution of
12x^3-23x^2-3x+2=0 is 2. Find all other solutions.
I tried rearranging the equation to factor by grouping, but that 23x^2 is bothersome and I can't get the right answers (I know the answers are 2, 1/4, and -1/3).
since you were told that x=2 is a solution, you know that x-2 must be a factor and must divide evenly into your expression.
So use either long division or synthetic division to change your equation to
(x-2)(12x^2 ...........) = 0
since your second factor is a quadratic you can use the quadratic formula to solve that.
(But since you know the solutions, we can conclude that the other factors have to be (4x-1)(3x+1) )