Final answer:
To find an expression for the missing dimension, we need to factor the volume expression. By factoring, we can determine the values of x that make the volume equal to zero, which represent the dimensions of the box.
Step-by-step explanation:
The volume of the box is given by the expression V=2x³-11x²+10x+8. In order to find an expression for the missing dimension, we need to factor the volume expression. By factoring, we can determine the values of x that make the volume equal to zero. These values will represent the dimensions of the box. So, let's factor the expression:
V=2x³-11x²+10x+8
By using synthetic division or factoring by grouping, we find the factors (x-2), (x-1), and (2x+4). Setting each factor equal to zero, we find that x=2, x=1, and x=-2. Therefore, the missing dimensions of the box are 2, 1, and -2.