If x = 3 x^2 + 11 - 2 , then the value of x3 + 5x2 + 12x is?

Answer: Option B

$$\begin{array}{rl}& x=\text{root}3\text{of}{x}^2+11-2\\ & \Rightarrow x+2=\text{root}3\text{of}{x}^2+11\\ & \Rightarrow \text{Taking cube on both side}\\ & \\ & \Rightarrow {\left(x+2\right)}^3=x^2+11\\ & \Rightarrow x^3+8+6x\left(x+2\right)=x^2+11\\ & \Rightarrow x^3+8+6x^2+12x=x^2+11\\ & \Rightarrow x^3+5x^2+12x=3\end{array}$$