a box in the shape of a rectangular prism has side lengths x, x+2, and x+10. Write a function, V(x), to express the volume of the box in ...?

V = LWH
V(x) = x(x+2)(x+10)
96 = x(x+2)(x+10)
x = 2 ... x+2 = 4 ... x +10 = 12

volume of the box
V(x) = x(x+2)(x+10) = x(x^2+12x+20)
V(x) = x^3+12x^2+20x
given volume = 96 cm^3, then
x^3+12x^2+20x-96=0
when x=2
2^2+12.2^2+20.2-96 = 8+48+40-96=0
thus (x-2) is a factor, to find other factors go by synthetic division method
2 | 1 12 20 -96
...| 0 2 28 96
----------------------------
...| 1 14 48 |0
----------------------------
(x-2)(x^2+14x+28)=0
x-2 = 0 or x+14x+28=0
x=2 is the only rational solution
the roots of x^2+14x+28=0 are irrational, thus the posible dimension of the cuboid
are 2 cm, 4 cm, 12 cm.