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## #1 2014-06-12 10:53:16

MathsIsFun
Registered: 2005-01-21
Posts: 7,686

### Coefficient vs Constant

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?

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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## #2 2014-06-12 10:59:47

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,858
Website

### Re: Coefficient vs Constant

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)``````

'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'
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## #3 2014-06-12 11:30:11

Agnishom
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From: Riemann Sphere
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### Re: Coefficient vs Constant

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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## #4 2014-06-12 12:00:30

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

### Re: Coefficient vs Constant

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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## #5 2014-06-12 12:30:58

MathsIsFun
Registered: 2005-01-21
Posts: 7,686

### Re: Coefficient vs Constant

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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## #6 2014-06-12 12:40:01

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

### Re: Coefficient vs Constant

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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## #7 2014-06-12 12:45:07

David
Member
From: Bumpkinland
Registered: 2014-04-23
Posts: 3,141

### Re: Coefficient vs Constant

A constant used to multiply a variable

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

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## #8 2014-06-12 12:47:13

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

### Re: Coefficient vs Constant

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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## #9 2014-06-12 12:48:07

David
Member
From: Bumpkinland
Registered: 2014-04-23
Posts: 3,141

### Re: Coefficient vs Constant

o.o How is that easy to understand?

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

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## #10 2014-06-12 12:50:26

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,858
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### Re: Coefficient vs Constant

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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## #11 2014-06-12 12:51:08

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

### Re: Coefficient vs Constant

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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## #12 2014-06-12 12:59:54

David
Member
From: Bumpkinland
Registered: 2014-04-23
Posts: 3,141

### Re: Coefficient vs Constant

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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## #13 2014-06-12 13:13:27

MathsIsFun
Registered: 2005-01-21
Posts: 7,686

### Re: Coefficient vs Constant

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.

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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## #14 2014-06-12 13:14:32

David
Member
From: Bumpkinland
Registered: 2014-04-23
Posts: 3,141

### Re: Coefficient vs Constant

Multiply what in algebra?

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

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## #15 2014-06-12 16:35:16

ganesh
Registered: 2005-06-28
Posts: 26,453

### Re: Coefficient vs Constant

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.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #16 2014-06-12 19:24:12

bob bundy
Registered: 2010-06-20
Posts: 8,427

### Re: Coefficient vs Constant

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

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy

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## #17 2014-06-12 19:48:27

MathsIsFun
Registered: 2005-01-21
Posts: 7,686

### Re: Coefficient vs Constant

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).

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

With an example.

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

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## #18 2014-06-12 20:09:47

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

### Re: Coefficient vs Constant

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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## #19 2014-06-12 20:27:20

MathsIsFun
Registered: 2005-01-21
Posts: 7,686

### Re: Coefficient vs Constant

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."

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

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## #20 2014-06-12 20:46:28

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

### Re: Coefficient vs Constant

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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## #21 2014-06-13 02:37:58

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

### Re: Coefficient vs Constant

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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## #22 2014-06-13 03:07:42

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,039

### Re: Coefficient vs Constant

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.

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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## #23 2014-06-13 03:08:40

ShivamS
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Registered: 2011-02-07
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## #24 2014-06-13 09:56:51

MathsIsFun
Registered: 2005-01-21
Posts: 7,686

### Re: Coefficient vs Constant

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?

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

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## #25 2014-06-13 11:02:23

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,039

### Re: Coefficient vs Constant

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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