Solve the polynomial by finding all roots
3x^3-8x^2+3x+2=0
I got so far
3x(x^2+1)-2(4x^2+1)
Thank you!
As you are finding out, grouping does not always work well.
The roots must be among ±1,±2, ±1/3, ±2/3
So, try the low-hanging fruit first, using synthetic division. That quickly gives you
(x-1)(3x^2-5x-2)
Then factor that, or use the quadratic formula to get
(x-1)(x-2)(3x+1)