What is a quadratic polynomial?

[Otis]

The lhs ... can be thought of as a polynomial with the correct u-substitution

I would've reworded that part, but I know what you mean.

 

[Otis]

Algebraic expression that constitutes the ordered sum or subtraction of a finite number of terms or monomials. They can have more than one variable

Is that your book's definition, or did you just copy that from some random web page (as is your habit)?

 

[eddy2017]

Is that your book's definition, or did you just copy that from some random web page (as is your habit)?

Algebra1 course 2 is the book I have. It has a definition for a polynomial function. Not for a polynomial.

 

[eddy2017]

But this definition is not fromcany website. It is from a rather reputable one.
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.
From Khan Academy .

 

[Steven G]

But this definition is not fromcany website. It is from a rather reputable one.
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.
From Khan Academy .

Well Khan is wrong! --if in fact he said that.
5 can NOT be written in the form k⋅xⁿ where n is a positive integer. Can you fix the mistake in the statement???
By the way, k⋅xⁿ is called a monomial. A polynomial is simply the sum of monomials.

 

[Steven G]

But this definition is not fromcany website. It is from a rather reputable one.
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.
From Khan Academy .

Can you supply the direct link to what you quoted? I doubt that Sal actually said that.

 

[eddy2017]

Can you supply the direct link to what you quoted? I doubt that Sal actually said that.

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

 

[eddy2017]

Lol

 

[Otis]

Algebra1 course 2 is the book I have. It has a definition for a polynomial function. Not for a polynomial.

Well, that's kind of silly. Perhaps, they've embedded the polynomial definition within the function definition.

Can you post a picture of their "polynomial function" definition? Thanks.

 

[eddy2017]

Read it and weep! Lol

 

[eddy2017]

If these books have these mistakes, can little old dum Eddy make one? Lollll.

 

[Otis]

I doubt that Sal actually said that.

Hard to say, Jomo. If he did, then I'm sure he didn't realize it. In videos, Sal regularly misstates bits of what he's written or he messes up writing bits of what he's said. After a number of years, he and his employees had begun adding corrections to many videos, but a lot of mistakes still remain. Sometimes, the site posts video corrections in writing, so one has to examine the entire web page.

Sal has so many employees now that it could be he hasn't even seen most printed information currently on his site. (They don't really moderate student claims in those 'conversation' sections, either, so those sections are also rife with misinformation.)

Read it and weep! Lol

Maybe you ought to weep a little, Eddy. Either you can't locate its quadratic definition or the book is deficient.

?

 

[Otis]

If these books have these mistakes, can little old dum Eddy make one? Lollll.

I'm glad you're joking because you've already answered that question for us many times over!

PS: I'm joking, too, lol.

[imath]\;[/imath]

 

[eddy2017]

I'm glad you're joking because you've already answered that question for us many times over!

PS: I'm joking, too, lol.

[imath]\;[/imath]

Yes, I was joking of course. What is the definition of a polynomial then?.

What is a polynomial?​

Polynomial are sums (and differences) of polynomial "terms".
For an expression to be a polynomial term, any variables in the expression must have whole-number powers (or else the "understood" power of 1, as in x1, which is normally written as x). A plain number can also be a polynomial term. In particular, for an expression to be a polynomial term, it must contain no square roots of variables, no fractional or negative powers on the variables, and no variables in the denominators of any fractions. Here are some examples:

Polynomials: Their Terms, Names, and Rules Explained

What is a polynomial? This lesson explains what they are, how to find their degrees, and how to evaluate them.

www.purplemath.com

 

[eddy2017]

Hard to say, Jomo. If he did, then I'm sure he didn't realize it. In videos, Sal regularly misstates bits of what he's written or he messes up writing bits of what he's said. After a number of years, he and his employees had begun adding corrections to many videos, but a lot of mistakes still remain. Sometimes, the site posts video corrections in writing, so one has to examine the entire web page.

Sal has so many employees now that it could be he hasn't even seen most printed information currently on his site. (They don't really moderate student claims in those 'conversation' sections, either, so they are also rife with misinformation.)


Maybe you ought to weep a little, Eddy. Either you can't locate its quadratic definition or the book is deficient.

?

no, that is the definiton in the book. you asked me to take a pic and send it. I did. Now what?. are these writers wrong too?.

 

[eddy2017]

Hard to say, Jomo. If he did, then I'm sure he didn't realize it. In videos, Sal regularly misstates bits of what he's written or he messes up writing bits of what he's said. After a number of years, he and his employees had begun adding corrections to many videos, but a lot of mistakes still remain. Sometimes, the site posts video corrections in writing, so one has to examine the entire web page.

Sal has so many employees now that it could be he hasn't even seen most printed information currently on his site. (They don't really moderate student claims in those 'conversation' sections, either, so those sections are also rife with misinformation.)


Maybe you ought to weep a little, Eddy. Either you can't locate its quadratic definition or the book is deficient.

?

The book is deficient, lol. And I don't boubt that for a second, believe. me!. I'll follow the definition from my tutors here. C'mon, what is that definition?. No one I have given seems to fit the bill.

 

[Otis]

any variables in [a polynomial] must have whole-number powers

Zero is a Whole number, and that's an issue with the definition above because x^0 is not defined when x itself is zero.

The definition above needs a bit of rewording. The exponents on variables need to be positive Integers (aka: Natural numbers).

 

[eddy2017]

Now we're talking!. Great. Thank you, Otis.

 

[Otis]

that is the definiton (sic) in the book ... are these writers wrong too?

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?

 

[Otis]

What is a polynomial?

Try the link below. I haven't thoroughly reviewed that page, but I see they make the same claim as purplemath. They say that x^0 is okay. I don't like that because it precludes x from taking on the value zero.

I searched the page for the word 'coefficient' and found it missing. I don't like that, either.

Polynomials

A polynomial looks like this ... Polynomial comes from poly- (meaning many) and -nomial (in this case meaning term) ... so it says many terms

www.mathsisfun.com