AMC 12 2022a Problem 15

The roots of the polynomial $10x^3-39x^2+29x-6$ are the height, length, and width of a rectangular box (right rectangular prism). A new rectangular box is formed by lengthening each edge of the original box by $2$ units. What is the volume of the new box?

$\textbf{(A) } \frac{24}{5} \textbf{(B) } \frac{42}{5} \textbf{(C) } \frac{81}{5} \textbf{(D) } 30 \textbf{(E) } 48$