Question 134150
If you are given that 2/3 is a root, then {{{x=2/3}}} => {{{3x=2}}} => {{{3x-2=0}}}, so {{{3x-2}}} is a factor of: {{{12x^3-77x^2+91x-30}}}


Using either polynomial long division or synthetic division, divide the cubic by the above derived factor.  Since the factor was derived from a root, the division will come out even, i.e. no remainder.  The quotient will be a quadratic that you can solve either by factoring, completing the square, or use of the quadratic formula.


Let me know if you need any help on any of these steps.