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Chapter 2: 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, as polynomial functions are defined for all real numbers. Therefore, there can't be a value for which the polynomial function is undefined.

Step by step solution

01

Identify the nature of Polynomial Functions

A polynomial function is a function that can be written in the form \(f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_2x^2 + a_1x + a_0\), where \(a_n, a_{n-1}, ..., a_2, a_1, a_0\) are real numbers, and each value of \(x\) represents a real number. The largest exponent, \(n\), is a non-negative integer and gives the degree of the polynomial.
02

Analyze the statement

By saying 'a polynomial inequality that has a value for which the polynomial function is undefined', it suggests there is \(x\) value that makes the polynomial function undefined. However, the initial definition of polynomial functions states that they are defined for all real numbers. This means for any real number that you substitute for \(x\), the polynomial will produce a valid real number as a result.
03

Conclusion

Thus, the statement 'I'm solving a polynomial inequality that has a value for which the polynomial function is undefined' does not make sense because polynomial functions are defined for all real numbers.

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