Solve the equation 9x^4-15x^3-5x^2+15x-4=0,if you know that it has at least one integer root

I did: (9x^4-15x^3-5x^2+15x-4)/(x-1)=9x^3-17x^2…

The answer should be: +/-1,1/3,4/3

f(x) = 9x^4-15x^3-5x^2+15x-4=0
Sum of coefficent = (9) + (-15) + (-5) + (15) + (-4) = 0 then x=1 is one of roots
Sum of coefficent(even power) = Sum of coefficent(odd power)
(9) + (-5) + (-4) = (-15) + (15) then x= -1 is one of roots
then we have:
g(x) = f(x)/[(x-1)(x+1)] = f(x)/(x²-1) = 9x² - 15x + 4
g(x)=0 then
9x² - 15x + 4 =0
x= 4/3 , x= 1/3

hence all of roots are : -1 , 1/3 , 1 , 4/3

What level of math is this? If it is at School level then I'll battle on, but if it's 2nd or 3rd year university level I won't battle on.

9x^4 - 15x^3 - 5x^2 +15x - 4 = 0.

I can't freaking do it! Damn. I need to know how to do these sort of equations as well. hmm..

>.<




*EDIT: The answer above me looks rightish. I've never seen that sort of method to working out a question like this though. Please tell me what level mathematics this is.



PLEASE! <3