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Chapter 3: Problem 95

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I'm solving a polynomial inequality that has a value for which the polynomial function is undefined.

Short Answer

Expert verified
The statement does not make sense because polynomial functions are defined for all real numbers, so there are no values for which the polynomial function is undefined.

Step by step solution

01

Understanding Polynomials

A polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s). By default, polynomials do not have any constraints, they are defined for all real numbers. This stems from their properties and the mathematical operations involved in them (addition, subtraction, multiplication and power of any whole numbers).
02

Investigating the Statement

The exercise provides a statement: 'I am solving a polynomial inequality that has a value for which the polynomial function is undefined.'.
03

Verifying the Statement

Based on our understanding of polynomials, we know that they are defined for all real numbers. This means that there should not be a value for which the polynomial function is undefined. The only exception would be if we are working with a ratio of polynomials, commonly referred to as a rational function, which can be undefined for certain values. However, in our case, the problem specifically mentions polynomial inequalities, not rational inequalities.

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