Final answer:
The sum of the degrees of each factor (1 + 1 + 3) is the degree of the polynomial for volume, resulting in the degree of the product being 5.
Step-by-step explanation:
Understanding the Degree of a Polynomial
The sum of the degrees of each factor is the degree of the product. In the provided example, length • width • height = (4x-1) • x • x³ results in a volume formula of 4x⁵ - x⁴. Here, the degrees of length, width, and height are 1, 1, and 3, respectively. The degree of the polynomial for volume, which is 5, corresponds to the sum of these degrees: 1 + 1 + 3. This reflects a fundamental concept in algebra known as the degree of a polynomial, which is essential when working with geometric formulas and dimensional analysis.
Geometric formulas such as cube volume (s³) and surface area (6s²), or sphere volume (4/3 pi r³) and surface area (4 pi r²), also follow this principle, where the degree of the polynomial corresponds to the dimensionality of the shape (2 for surface area, 3 for volume).