What is a quadratic polynomial?

[Otis]

0^0 is a mathematical expression with no agreed-upon value

Clearly, but I'm pushing for an agreed-upon definition -- at least at the beginning algebra level.

Like other contradictory statements in math, I think exceptions ought to be revealed to students up front (whatever the level in which they're introduced) -- even when they don't apply to the current course.

Another example: zero is neither positive nor negative._(EDITED) That's not always true, and students ought to be told that they might see exceptions to that "rule", later.

I've had so many teachers say, "never do that", only to see "that" done in later courses without so much as a peep. That may be confusing. (Undeclared exceptions to information that was presented as "rules carved in stone" used to drive me nuts, until I eventually learned that not all math is consistent.)

 

[eddy2017]

Holy Cow!. Lol

 

[eddy2017]

Otis said:
I would replace "an algebraic expression" with "a polynomial.
And that makes a world of sense to me because it avoids a lot of confusion.thanks!

 

[Dr.Peterson]

Clearly, but I'm pushing for an agreed-upon definition -- at least at the beginning algebra level.

Which Wikipedia, at least, says we have: 1. Of course, not everyone does agree ... but do they ever?

Like other contradictory statements in math, I think exceptions ought to be revealed to students up front (whatever the level in which they're introduced) -- even when they don't apply to the current course.

Agreed. What I say, when I have reason to at this level, is that there are some problems with 0^0, but in our context we take it to be 1, largely because that lets us say that the degree of the constant term in a polynomial is 0.

Another example: zero is neither even nor odd. That's not always true

Who says that? I'd say that's never true. I can't think of any reason to say it isn't even, except perhaps not to list it as even when the context covers only positive integers. Now I'm curious.

 

[Otis]

Some teachers also [mentioned] integrate using U-substitution? Is [that] correct?

Yes. A u-substitution step may be used in various branches of mathematics (not just beginning algebra). It's done mostly to obtain a new function or expression (i.e., different form) for which we have a way to proceed. If you want to watch videos using u-substitution to solve certain higher-order polynomial equations, then watching videos on integration techniques probably won't help.

Be more specific, when using keywords in a search (eg: solve polynomiaIs u-substitution). I'll post a link below, but in the meantime I don't think you need a video to try u-substitution on the first example that Jomo had posted. I'd already given you the two substitutions to make.

Finding 4th-degree polynomial roots using u-substitution.

 

[Otis]

zero is neither even nor odd.

Who says that?

Just me, I hope. heh

I'd realized right after posting that I'd botched my example, but, when I'd clicked 'Edit', the server kicked me off the site and would not let me back in. That's five times in three days now, twice in the last 90 minutes, ugh. (I think it's almost time for me to put this forum in my rearview mirror.)

Anyhoo, I'd meant to say "neither positive nor negative". My apologies.

 

[Deleted member 4993]

However:

0! = 1 .......................... to keep the definition of combination alive.

 

[Deleted member 4993]

Just me, I hope. heh

I'd realized right after posting that I'd botched that example, but, when I'd clicked 'Edit', the server kicked me off the site and would not let me back in. That's five times in three days now, twice in the last 90 minutes, ugh. (I think it's almost time for me to put this forum in my rearview mirror.)

Anyhoo, I'd meant to say "neither positive nor negative". My apologies.

I have not been "kicked-out" yet ............ but I wonder if it is a location/browser problem. I am using chrome without any interruption.

(I think it's almost time for me to put this forum in my rearview mirror.)

Nooooo .... don't do that Harry-the-Cat will be very sad.... including me......

 

[eddy2017]

I have not been "kicked-out" yet ............ but I wonder if it is a location/browser problem. I am using chrome without any interruption.


Nooooo .... don't do that Harry-the-Cat will be very sad.... including me......

And little old dum Eddy too!!!.

 

[Harry_the_cat]

Nooooo .... don't do that Harry-the-Cat will be very sad.... including me......

Why will I be sad? Sorry, I've been away for a week in beautiful Tasmania and have totally missed this thread (which I think is a good thing!).

 

[Deleted member 4993]

Why will I be sad? Sorry, I've been away for a week in beautiful Tasmania and have totally missed this thread (which I think is a good thing!).

Well - if Otis-the-cat retires from this site - you will lose your only feline companion in this forum.

Did you meet the Tasmanian Devil during your trip to southern south?

 

[Otis]

been away for a week in beautiful Tasmania

Hunting tourists who harass the wombats?

?

 

[Harry_the_cat]

Well - if Otis-the-cat retires from this site - you will lose your only feline companion in this forum.

Did you meet the Tasmanian Devil during your trip to southern south?

Oh yes I see what you mean! ?
No, didn't encounter any devils this time!

 

[Steven G]

A mo

A monomial simply put is an algebraic expression that has only one term
And that is my own definition. Did not copy it from any website. Lol
Some examples to boot -5m^7, 35b^3, 4x^2, 2ab^2
And two monomials make a binomial and three make a trinomial.

No, that is not the correct definition of a monomial! You were supposed to fix Khan's definition.
A monomial is a single term in the for of a*x^n where a is any real number and n is a non-negative integer.
A polynomial is the sum of many monomials.

 

[eddy2017]

No, that is not the correct definition of a monomial! You were supposed to fix Khan's definition.
A monomial is a single term in the for of a*x^n where a is any real number and n is a non-negative integer.
A polynomial is the sum of many monomials.

Wow, that has a nice ring it!. Thank you!. It goes onto my note book.

 

[Otis]

A monomial is a single term in the [form] of a*x^n where a is any real number and n is a non-negative integer.

If you're going to include the possibility of 0^0=1, then you ought to define x^0=1 for all Real values of x.

Also, a monomial may contain multiple variables.

A polynomial is the sum of many monomials.

Not all polynomials are a sum of "many" monomials. The number of monomials comprising a sum may be two or more. Some polynomials are not a sum at all -- they consist of a single monomial.

I like how the polynomial/monomial definition in Eddy's book treats constants and variables separately (hence, no possibility of 0^0), while also allowing single constants as monomials. Unfortunately, the book's definition places no restrictions on the exponents.

?

 

[eddy2017]

Jomo, the ball is in your court. And it has quite a topspin!. Lol.

 

[mmm4444bot]

Jomo, the ball is in your court. And it has quite a topspin!. Lol.

There are certainly nuances in mathspeak, Eddy, but I think the tutors are more interested in the ball that you started bouncing (to learn about quadratic equations).

Did you check your second book (Algebra 2), to see whether the word 'quadratic' appears in the index?

?

 

[eddy2017]

Hey, mmm, sorry. I was joking a little bit with the profs because out of their conversation I learn a lot.
Yes, Quadratic equations are in the book. I'm attaching a pic here. I sent you a PM about an equation solver you offered to send me if I thought I nedeed it. Please, please, if that offer is still on, I will accept it. Please. Even if I have to pay for it. Send it to me and tell me how much it cost ( or wait till I send you the money. Consider it a small contribution to a site which helps everyone so much!) and then send it. However way you think it is best. I would love to have that. You talked about how simple and effective itcwas and how good it managed the grouping symbols.
Here's the pic. I'm studying this book.

 

[eddy2017]

It is a very good book. I'm getting a lot out of it. Thank you for asking and for caring.