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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,608

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.)

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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)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,832

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.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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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 ... ?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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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.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,832

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.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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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.'

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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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.

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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).

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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.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,792

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****Moderator**- Registered: 2010-06-20
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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: 7,608

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****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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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.**

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**MathsIsFun****Administrator**- Registered: 2005-01-21
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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****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,832

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.**

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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: 16,015

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: 16,015

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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