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Determining if is a Factor of Using the Factor Theorem
To determine if is a factor of the polynomial function using the Factor Theorem, evaluate the function at the corresponding value of . For the binomial , the value is . Substitute into the function: . Evaluate the exponent to obtain , which simplifies to . Because the function evaluates to , the Factor Theorem confirms that is a factor of .
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Ch.5 Polynomials and Polynomial Functions - Intermediate Algebra @ OpenStax
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Determining if is a Factor of Using the Factor Theorem
Determining if is a Factor of Using the Factor Theorem
Determining if is a Factor of Using the Factor Theorem
A chemical engineer uses a polynomial function to model the concentration of a substance in a reaction at time . If the engineer observes that the concentration is zero at seconds (meaning ), which expression must be a factor of the polynomial according to the Factor Theorem?
An analyst uses a polynomial function to model the revenue of a product based on its price . If the analyst finds that the revenue is zero when the price is 15 dollars (meaning ), the Factor Theorem states that is a factor of the revenue function.
Factor Theorem in Structural Modeling
In your role as a business analyst, you are using polynomial functions to model sales data and identify break-even points where profit is zero. Match each observed data point or algebraic property of the profit model with its equivalent implication according to the Factor Theorem.
You are an inventory analyst using a polynomial model, , to forecast warehouse stock levels over time . If you determine that the inventory hits exactly zero at a specific time (meaning ), the Factor Theorem guarantees that the binomial expression must be a ____ of the polynomial function .
Learn After
As a packaging engineer, you model the capacity of a shipping container using the cubic function . You need to verify if an inner dimension represented by perfectly divides this volume. Arrange the steps in the correct order to recall and apply the Factor Theorem for this specific volume model.
A quality control engineer uses the function to model the volume of a precision-cut component. According to the Factor Theorem, which value of should the engineer substitute into the function to determine if the dimension is a mathematical factor of this volume model?
A logistics coordinator uses the function to model the volume of a standardized shipping container. To verify if a smaller packing unit with dimension is a mathematical factor of this volume using the Factor Theorem, the coordinator calculates . According to the theorem, what numerical value must result in to confirm that is a factor?
A design engineer uses the polynomial to model the capacity of a precision component. To determine if the dimension is a factor of this model, the engineer applies the Factor Theorem. Match each component of the mathematical evaluation with its correct value or conclusion.
A fabrication specialist uses the polynomial to model the volume of a precision-cut metal block. According to the Factor Theorem, if the specialist evaluates the function at and determines that , then the expression is a factor of the volume function.