Final answer:
Box 1's volume is a single-term polynomial, specifically a monomial, while Box 2's volume is a two-term polynomial, known as a binomial. Each volume is found by multiplying the area of the base by the height.
Step-by-step explanation:
The question involves calculating the polynomial volume expressions for two geometric boxes and determining the number of terms in each polynomial. To find the polynomial representing the volume, we multiply the area of the base by the height for each box.
For Box 1, with dimensions x by 3x by x³, the area of the base is given by multiplying the length and width: Area of base = x(3x) = 3x².
Since the height is x³, the volume is: Volume = Area of base * Height = 3x² * x³ = 3x²³ = 3x⁵.
This is a single-term polynomial, also known as a monomial.
For Box 2, with dimensions x by 4x-1 by x³, the area of the base is x(4x-1) = 4x² - x.
Multiplying this area by the height x³ gives us the volume: Volume = (4x² - x) * x³ = 4x²³ - x´.
This results in a two-term polynomial, known as a binomial.