AMC 10/12A 2022 (Problem 16)

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?

\text{(A)}\;\frac{24}{5}

\text{(B)}\;\frac{42}{5}

\text{(C)}\;\frac{81}{5}

\text{(D)}\;30

\text{(E)}\;48