Find the remainder when 3x3 + 6x - 1 is divided by x - 3.

Step 1: Identify the polynomial and the divisor. The polynomial is $P(x) = 3x^3 + 6x - 1$. The divisor is $x - 3$.

Step 2: Apply the Remainder Theorem. According to the Remainder Theorem, if a polynomial $P(x)$ is divided by $x - c$, the remainder is $P(c)$. In this case, $c = 3$. So, we need to find $P(3)$.

Step 3: Substitute $x = 3$ into the polynomial. $P(3) = 3(3)^3 + 6(3) - 1$

Step 4: Calculate the value. $P(3) = 3(27) + 18 - 1$ $P(3) = 81 + 18 - 1$ $P(3) = 99 - 1$ $P(3) = 98$

The remainder is $98$.

The final answer is $\boxed{98}$.