Answer:
Quotient =(3x²-5x-1) and reminder = 1
Explanation:

3x-1)9x³-18x²+2x+2(3x²-5x-1
 9x³-3x²
 ------------------------
 -15x²+2x+2
 -15x²+5x
 ------------------
 -3x+2
 -3x+1
 --------
 1
Therefore 9x³-18x²+2x+2=(3x²-5x-1)(3x-1)+1
Quotient =(3x²-5x-1) and reminder = 1