Given that 1 is a zero of p(x)=3x^4-x^3-8x^2+2x+4, factor the polynomial completely, and then list all its zeros.

Divide p over (x-1) with euclidian division we get the quotient:

Note that -2/3 is also roots of the above polynomial. 
Checking:

Dividing again with euclidian algorithm we get the quotient:
over  is .
Final factorization: