Question

How does unit analysis justify the multiplication of two polynomial models representing real-world quantities?

A) By ensuring that the units of the resulting expression match the expected units
B) By verifying that the exponents in the polynomial models align mathematically
C) By confirming that the coefficients of the polynomials have appropriate unit ratios
D) By comparing the degrees of the polynomials and ensuring consistency

Answer 1

Unit analysis justifies the multiplication of two polynomial models by ensuring that the units of the resulting expression match the expected units.

Step-by-step explanation:

Unit analysis, also known as dimensional analysis, allows us to justify the multiplication of two polynomial models representing real-world quantities by ensuring that the units of the resulting expression match the expected units. This is option A of the given choices. Let's consider an example:

Suppose we have a polynomial model for the speed of a car in miles per hour (mph) which is represented as 3x^2, and another polynomial model for the time in hours which is represented as 2x+1. To find the distance traveled by the car, we can multiply these two polynomials:

(3x^2)(2x+1). By applying unit analysis, we can see that the units of the resulting expression will be miles (distance) as the x terms cancel out the units of hours, and the coefficient 3 has units of miles per hour which aligns with the expected units. Therefore, the unit analysis justifies the multiplication of these polynomial models.