h(x) Not A Polynomial Function

mathdad

mathdad

Full Member
Joined
Apr 24, 2015
Messages
925
Given h(x) = (x^2 - 2)/(x^3 - 1), Sullivan states the following:

"h is not a polynomial function. It is the ratio of two distinct polynomials, and the polynomial in the denominator is of positive degree."

1. I understand h to be a rational function.

2. What if the polynomial in the denominator is of negative degree or zero degree? Does it then qualify to be called a polynomial function?

Thank you.

P. S. I did say yesterday no more math questions until next Tuesday. This is true. I do not consider any of my posts today to be actual math questions. I am simply trying to make sense of several comments made by Sullivan in the beginning of section 5.1, Polynomial Functions and Models. Have a good day.
 
There is no negative degree for a polynomial. Do you see why, from the definition?

A zero degree polynomial would be a constant. Yes, it can still be called a polynomial, though it is a trivial one. So (x^2 - 2)/3 is a rational function; in fact, so is any polynomial, as it can be written as, say, (x^2 - 2)/1 !

I'm not sure of the point of mentioning "positive degree", since you didn't show the context.
 
I am willing to bet that the book gives definitions. If your questions about polynomials quoted the relevant definitions from the book, I bet the answer to these questions would be virtually self-evident..
 
JeffM said:
I am willing to bet that the book gives definitions. If your questions about polynomials quoted the relevant definitions from the book, I bet the answer to these questions would be virtually self-evident..
Click to expand...

Self-evident to you not to me.
 
Excuse me, but you were asked politely to show the definition that is in your book. Why do you choose not to?

I want to be very clear about something. When someone here asks you a question there is a reason why they asked it. You may not see what the tutor is getting at but the tutor has a clear reason for asking.

I remember someone telling me you know that 1+1 equals 2 and then I realized something about counting all subsets of a set.

Now go and supply JeffM with his definition and answer my questions from a previous post.
 
Jomo said:
Excuse me, but you were asked politely to show the definition that is in your book. Why do you choose not to?

I want to be very clear about something. When someone here asks you a question there is a reason why they asked it. You may not see what the tutor is getting at but the tutor has a clear reason for asking.

I remember someone telling me you know that 1+1 equals 2 and then I realized something about counting all subsets of a set.

Now go and supply JeffM with his definition and answer my questions from a previous post.
Click to expand...

Sorry. I am moving on. I got the answer I needed from another site without the burden of trying to be perfect, which I am not.
 
mathdad said:
... I got the answer I needed from another site without the burden of trying to be perfect ...
Click to expand...
I'm glad to hear that you got what you needed. I hope they can help you again! Cheers

?
 
Otis said:
I'm glad to hear that you got what you needed. I hope they can help you again! Cheers

?
Click to expand...

If I do not get here, I can go somewhere else. You see, I work 40 plus hours a week. In fact, I took a little break at the job RIGHT NOW to check FMH. I just do not have enough time to learn theory and the THE WHY AND PROOFS that college students majoring in math must learn. I post my questions with work shown. I just want the solution steps to guide me to the answer. I AM NOT ASKING ANYONE HERE TO DO THE MATH WORK FOR ME.
 
mathdad said:
... . I just do not have enough time to learn ... THE WHY ... I just want the solution steps to guide me to the answer. I AM NOT ASKING ANYONE HERE TO DO THE MATH WORK FOR ME.
Click to expand...
Please calm down. There's no reason to shout at us.

A list of steps without the math hasn't worked for you, in the past. Neither has tutoring, in general. I'm reviewing your theads from years past, at those other sites. You've been going around in circles. You don't seem to pay attention to the guidance you're given.

If you are serious in saying that you want replies containing a description of the steps only and no math workings shown, please state this in your ops. (I had no clue about this because I haven't seen you mention it before, here or at other forums.)

\(\;\)
 
Otis said:
Please calm down. There's no reason to shout at us.

A list of steps without the math hasn't worked for you, in the past. Neither has tutoring, in general. I'm reviewing your theads from years past, at those other sites. You've been going around in circles. You don't seem to pay attention to the guidance you're given.

If you are serious in saying that you want replies containing a description of the steps only and no math workings shown, please state this in your ops. (I had no clue about this because I haven't seen you mention it before, here or at other forums.)

\(\;\)
Click to expand...

I will request solution steps for me to try on my own.
 
Jomo said:
Excuse me, but you were asked politely to show the definition that is in your book. Why do you choose not to?

I want to be very clear about something. When someone here asks you a question there is a reason why they asked it. You may not see what the tutor is getting at but the tutor has a clear reason for asking.

I remember someone telling me you know that 1+1 equals 2 and then I realized something about counting all subsets of a set.

Now go and supply JeffM with his definition and answer my questions from a previous post.
Click to expand...

I will give the definition as stated in Sullivan's book from now. As far as this question is concerned, I am beyond this section in the book. It is a good idea to include the definitions and correct wording as stated by Sullivan and others.
 
You must log in or register to reply here.
Top