Question

Dimensions: x by 3x by x3

Answer 1

Box's 1 volume will be a monomial
box's 2 volume will be a binomial 
 The reasoning is because box 1's volume is model by a monomial times a monomial, so it will be a monomial. 
  Box 2's volume is modeled by a monomial times a binomial, so it will be a binomial

Answer 2

Box #1:
Dimensions are x, 3x,  and x³.
Base area, A = x*(3x) = 3x².
Volume, V = (3x²)*(x³) = 3x⁵.
The volume is a 5-th order polynomial. It has only one term, which is the leading term.

Box #2:
Dimensions are x, (4x-1), and x³.
Base area, A = x*(4x-1) = 4x² - x.
Volume, V = (4x² - x)*(x³) = 4x⁵ - x⁴.
The volume is a 5-th order polynomial. It has two terms. 
It could be written as
V(x) = 4x⁵ - x⁴ + 0x³ + 0x² + 0x¹ + 0x⁰.
Only terms involving x⁵ and x⁴ have non-zero coefficients.