What is a quadratic polynomial?

[eddy2017]

The definition is mostly good, for a polynomial. However, they need to include a statement about the exponents.

As far as defining the function part, their definition is completely lacking.

By the way, does the word 'quadratic' appear in that book's index?

No, it doesn't. It was the first thing I looked up. It is not there. Strange!. Algebra 1 course and they talk about Polynomials but nothing about QE.

 

[eddy2017]

I said I followed your definition because I was not either joking or using flattery when I said your knowledge
( all tutors and profs here) is fantastic, to say the least. I'll check the link tomorrow. It is sort of late now. Thanks for the replies.

 

[Steven G]

Polynomials intro (video) | Khan Academy

Polynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer. For example, 3x+2x-5 is a polynomial. Introduction to polynomials. This video covers common terminology like terms, degree, standard form, monomial, binomial and trinomial.

www.khanacademy.org

Sal has an error on that page.
As I asked you, can you fix the mistake? How can 5 be in the form of k⋅xⁿ

 

[Otis]

Strange!. Algebra 1 course and they talk about Polynomials but nothing about QE

It's not uncommon for texts to use some vocabulary without defining it. Same goes for math expressions; you might see quadratic polynomials in a chapter on factoring, but they haven't named them as such. Maybe they discuss solving 2nd-degree polynomial equations in Algebra 2.

[imath]\;[/imath]

 

[eddy2017]

No, you can not.

All quadratic polynomials can be written as ax^2+bx+c.

There will never be any exponent larger than 2, in a quadratic polynomial. That's the definition! Quadratic polynomials are second-degree polynomials.

Maybe you are conflating the names 'quadratic polynomial' and 'quadratic form'. They do not mean the same thing.

---

Some polynomials containing an x^7 term may be expressed in quadratic form, but only by changing the inputs (eg: u-substitution). Whenever we do that, we are switching to a new function. We are not changing the original polynomial into a quadratic; we are simply using a quadratic form to help us obtain information about the original, higher-order polynomial.

Did you try the u-substitution example, that I'd suggested. If so, then what did you get?

One question Otis, before I attempt the u-substitution you asked me to do.
Some teachers also called this operation: integrate using U-substitution?. Is the this correct?.
I want / need to watch a couple of tutorials.

 

[lev888]

One question Otis, before I attempt the u-substitution you asked me to do.
Some teachers also called this operation: integrate using U-substitution?. Is the this correct?.
I want / need to watch a couple of tutorials.

Nowhere in this thread "integrate using U-substitution" was mentioned. What are you referring to?

 

[eddy2017]

Okay please, let's forget then about what I asked. It was a tutorial that came up when I typed in u substitution in Google box. I got it now that it is not the same thing. Lev, your reply answered my question

 

[eddy2017]

This one is the one I need to study.

 

[eddy2017]

Solving equations in Quadratic form using U-substitution.

 

[eddy2017]

Sal has an error on that page.
As I asked you, can you fix the mistake? How can 5 be in the form of k⋅xⁿ

I'm working on it.

 

[Steven G]

I'm working on it.

Hint: 5 = 5*x⁰

 

[Otis]

5 = 5*x^0

That's correct, as long as x never equals zero.

 

[eddy2017]

That's correct, as long as x never equals zero.

well, x to the 0 power= 1
5= 5(1)
5=5

 

[Steven G]

....so what is the definition of a monomial---remember Subhotosh's nephew, Sal Khan, gave you the wrong definition.

 

[Steven G]

well, x to the 0 power= 1
5= 5(1)
5=5

No! Otis just told you that x to the 0 power is NOT 1 if x=0. So stop saying that x⁰=1!!!

 

[eddy2017]

A mo

....so what is the definition of a monomial---remember Subhotosh's nephew, Sal Khan, gave you the wrong definition.

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.

 

[eddy2017]

No! Otis just told you that x to the 0 power is NOT 1 if x=0. So stop saying that x⁰=1!!!

If x = 0 then
0 to the power of 0 = 1
Then that would make the equation true
5 * 1= 5
5=5
If it is not like that then I do not know. Can't think of anything else.

 

[Otis]

0 to the power of 0

The expression 0^0 is undefined, Eddy (just like division by zero is undefined).

However, any other Real number raised to the exponent zero does equal 1. That is one of the properties of exponents to memorize.

Therefore, when we write a variable raised to the exponent zero, then we also need to declare in our work that the variable does not equal zero.

[imath]x^0 = 1, \quad x \ne 0[/imath]

Unfortunately, a lot of school materials fail to include the condition [imath]x \ne 0[/imath].

?

 

[Dr.Peterson]

The expression 0^0 is undefined, Eddy (just like division by zero is undefined).

However, any other Real number raised to the exponent zero does equal 1. That is one of the properties of exponents to memorize.

Therefore, when we write a variable raised to the exponent zero, then we also need to declare in our work that the variable does not equal zero.

[imath]x^0 = 1, \quad x \ne 0[/imath]

Unfortunately, a lot of school materials fail to include the condition [imath]x \ne 0[/imath].

?

It's actually a little more subtle than that:

Zero to the power of zero - Wikipedia

en.wikipedia.org

Zero to the power of zero, denoted by 0⁰, is a mathematical expression with no agreed-upon value. The most common possibilities are 1 or leaving the expression undefined, with justifications existing for each, depending on context. In algebra and combinatorics, the generally agreed upon value is 0⁰ = 1, whereas in mathematical analysis, the expression is sometimes left undefined. Computer programming languages and software also have differing ways of handling this expression.​

 

[Otis]

A monomial simply put is an algebraic expression that has only one term

I would replace "an algebraic expression" with "a polynomial".

That way, you inform the reader that you're specifically talking about polynomial terms, and not all manner of algebraic terms like 4/x or x^(1/2).

And, you would of course need to have the polynomial definition on hand, before defining monomials, binomials and trinomials as polynomial terms.

I like the polynomial definition in your book, but it's missing a statement that restricts exponents to positive Integers.