Dimensions: x by 3x by x3

Area of base = x (3x) = 3x2

Box 2: Dimensions: x by 4x - 1 by x3

Area of base = x (4x - 1) = 4x2 - x

Complete the statements about the number of terms in the polynomial representing the volume of each box.

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

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.