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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,684

On the website I define a coefficient as "A number used to multiply a variable"

So, in

3 and 7 are coefficients and 2 is a constant. But is 2 also a coefficient?

How about in

Are a, b and c all coefficients?

(I want the simplest accurate definition.)

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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IMHO, it is. It is the coefficient of x^0

Go to sagecell.sagemath.org and run this code:

```
x = var('x')
expand((1+x)^6).coeff(x,n=0)
```

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Wikipedia agrees too. http://en.wikipedia.org/wiki/Coefficient

Down the article, you have:

for some integer , where are coefficients; to allow this kind of expression in all cases one must allow introducing terms with 0 as coefficient.

*Last edited by Agnishom (2014-06-12 11:30:43)*

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

It is a coefficient.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**MathsIsFun****Administrator**- Registered: 2005-01-21
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So, what is a good and easy to understand (for adults and children) definition of coefficient ... ?

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

That is a good question. I do not know of a simple definition. Wiki takes 2 pages for it.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,136

A constant used to multiply a variable

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Wikipedia uses:

In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series or any expression; it is usually a number, but in any case does not involve any variables of the expression.

The constant term is a coefficient as said already:

Enter this at Wolfram Alpha:

Coefficientlist of x^2 + 3x -8

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
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o.o How is that easy to understand?

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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MathsIsFun wrote:

So, what is a good and easy to understand (for adults and children) definition of coefficient ... ?

A coefficient of a variable in some polynomial term is the constant by which it has been multiplied.

*Last edited by Agnishom (2014-06-12 12:50:48)*

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

That is what I am saying it is not easy. He will have to go into explaining that the -8 in x^2 + 3x -8 is a coefficient even though you do not see any variable connected to it.

Also, it does not have to be a polynomial:

The 2 and the -6 are coefficients.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,136

This one is from google : 1.

MATHEMATICS

a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g., 4 in 4x y).

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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**MathsIsFun****Administrator**- Registered: 2005-01-21
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Yes, we normally draw a distinction between coefficient and constant, but then a constant is also a coefficient. A bit like a square is a rectangle.

How about

A number (or other fixed value) used to multiply in algebra.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
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Multiply what in algebra?

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 23,792

Hi MathsIsFun,

I learned in my school days, in the quadratic equation

a,b are coefficients; c is a constant and x (and y, z) are variables.

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,228

hi MathsisFun,

Looking around the internet, there doesn't seem to be consistency about whether the constant term is a coefficient. I suggest we say it is. As to a formal definition, it is very hard to do this in a simple way. Why bother? If you give examples, then it becomes clear. And if you say the coefficient c in ganesh's post is also often called the constant term, then you've covered it either way and alerted readers to the 'debate'.

Bob

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,684

Yes, it seems there is not consensus.

I do feel that having a constant also be a coefficient is more elegant (like a square being a rectangle).

How about

"The number (or other fixed value) part of a term."

With an example.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

A good example will make it all clear.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,684

OK, this is the new wording (so far), improvements welcome!

"The number (or other fixed value) part of a term, such as the 4 in 4y

A constant can also be though of as a coefficient. In ax² + bx + c, a, b and c are coefficients."

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

That is okay as far as it goes as long as you do not forget the t in thought. Post #11 shows one problem with that definition. Combinatorics and generating functions sort of make it easy to see that the constant term is a coefficient but a coefficient of what? In ax^2 + bx + c you say c is a coefficient of x^0 but in x + y + z +3 what is the 3 a coefficient of? x^0 or y^0 or (xy)^0. That might be difficult to explain.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

MathsIsFun wrote:

Are a, b and c all coefficients?

In my opinion (along with asking a few professors here for their opinions), a and b are coefficients of x^2 and x respectively and c of x^0. However, we can't say that c is a coefficient in ax^2 + bx + c, but we can say it is in ax^2 + bx + cx^0.

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,037

The way I understand it:

1) c is a coefficient in that polynomial;

2)coefficient is a constant used in a polynomial. I have not seen the term coefficient used much elsewhere.

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**ShivamS****Member**- Registered: 2011-02-07
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**MathsIsFun****Administrator**- Registered: 2005-01-21
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ShivamS wrote:

However, we can't say that c is a coefficient in ax^2 + bx + c, but we can say it is in ax^2 + bx + cx^0.

That makes sense.

What does everyone think about that?

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,037

I think it's a bit confusing considering the two are the same. And I'd rather call it a coefficient than not.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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