Use the long division method to find the result when $9 x^{3}+6 x^{2}+28 x+9$ is divided by $3 x+1$. Answer Atempt iout of:

Step 1 ：\(\frac{9x^3}{3x} = 3x^2\)

Step 2 ：\((9x^3 + 6x^2) - (3x^2(3x+1)) = 3x^2 + 28x + 9\)

Step 3 ：\(\frac{3x^2}{3x} = x\)

Step 4 ：\((3x^2 + 28x + 9) - (x(3x+1)) = 27x + 9\)

Step 5 ：\(\frac{27x}{3x} = 9\)

Step 6 ：\((27x + 9) - (9(3x+1)) = 0\)

Step 7 ：\(\boxed{3x^2 + x + 9}\)