Learn Before
Division of Polynomial Functions
For polynomial functions and , where , their division is defined by the formula . This means that to find the quotient function, you set up a rational expression with the polynomial for in the numerator and the polynomial for in the denominator. The resulting expression can then be simplified using polynomial division.
0
1
Tags
OpenStax
Intermediate Algebra @ OpenStax
Ch.5 Polynomials and Polynomial Functions - Intermediate Algebra @ OpenStax
Algebra
Related
Independent Variable of a Mathematical Function
Dependent Variable of a Mathematical Function
Evaluating a Mathematical Function
Graph of a Mathematical Function
Multiplication of Polynomial Functions
Division of Polynomial Functions
A shipping coordinator at a logistics company uses a mathematical function named to calculate the total shipping cost based on the package weight, . Match each part of the function notation with its correct mathematical description according to the rules of function notation.
An office manager uses a function to determine the number of toner cartridges to order based on the number of documents printed each month. In the notation , what does the variable represent?
A payroll clerk uses the notation to represent the gross pay for an employee who has worked hours. True or False: In this mathematical notation, the parentheses indicate that the function name is being multiplied by the number of hours .
Verbalizing and Categorizing Function Notation
An inventory analyst at a retail distribution center is reviewing a system algorithm that calculates restock quantities. The system uses a mathematical function named , where the restock quantity depends on the current inventory level , written as . According to the rules of function notation, the variable represents the ________ value, while represents the corresponding range value.
Interpreting Production Cost Function Notation
Interpreting Utility Billing Function Notation
Learn After
Finding the Quotient of Polynomial Functions and Evaluating at
A business operations manager uses the polynomial function to represent a company's total monthly operating costs and the polynomial function to represent the number of units produced. To determine the average cost per unit, the manager needs to define the quotient function . According to the definition of the division of polynomial functions, which formula correctly represents this function?
A logistics analyst for a shipping firm is modeling 'Fuel Efficiency' by dividing the total fuel cost polynomial, , by the total mileage polynomial, . Match each component of the mathematical model with its correct role in the definition of the quotient function .
True or False: In a business analytics model, a manager uses the polynomial function to represent total revenue and to represent total expenses. According to the formal definition of the division of polynomial functions, the quotient function (R/E)(x) = rac{R(x)}{E(x)} is mathematically defined for all values of , including those where the expense polynomial is equal to zero.
Defining the Average Unit Revenue Quotient Function
A logistics coordinator for a shipping firm is modeling 'Worker Productivity' by dividing a 'Total Items Processed' polynomial by a 'Total Labor Hours' polynomial . Arrange the following steps in the correct order to formally define the quotient function according to the definition of the division of functions.
A retail store manager uses the polynomial function to model total weekly sales revenue and the polynomial function to model total hours worked by staff. To analyze productivity, the manager defines the sales-per-hour quotient function, . According to the formal definition of the division of polynomial functions, the polynomial representing total weekly sales, , must be placed in the ____ of the rational expression.