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I was studying about polynomials when I stumbled upon this video

https://www.youtube.com/watch?v=vBfdYuoc3x4&list=PLjS5lmipV2HJEaKfdeVSKdprfFxinzmNw&index=2

The video says that a monomial has three parts -- constant, variables, and exponent. But I remember my teacher said it was coefficient.

Was my teacher wrong? Should I ask her if constant is same as coefficient?

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    $\begingroup$ $5x^3$. In this case, the coefficient $5$ is a constant. In other situations, these two words may not have the same meaning. $\endgroup$ Aug 4 at 15:53
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    $\begingroup$ I've added the (terminology) tag. That said, I've also voted to close since I feel this is more a learner's question to be asked on math.stackexchange.com than here. $\endgroup$
    – J W
    Aug 5 at 11:25
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    $\begingroup$ You should definitely ask your teacher, in addition to reading the replies here. That's the kind of thing she is there for. Of course, don't ask it in the form: "The internet says you are wrong, defend yourself!" but rather something more like: "I've seen another term used for this same thing, can you help me understand why they did that?" $\endgroup$
    – Adam
    Aug 5 at 14:42
  • $\begingroup$ Your teacher is not wrong. Generally the constants in front of the $x$ terms are indeed called coefficients (the constant in front of the $x^0$ term, which is hardly ever written, is what's usually called the constant.) I'm not making this an answer because it's a terminology question and terminology varies. $\endgroup$
    – Thierry
    Aug 6 at 16:40
  • $\begingroup$ Also, if we're calling coefficients constants, why not call the exponents constants as well? So really the three parts are constant, variable, constant. $\endgroup$
    – Thierry
    Aug 6 at 16:43

2 Answers 2

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I'd say that the video is not using the best word. I would call that constant the coefficient.

Constant means that it is a number and not a variable. That's true. But the word coefficient conveys more meaning. It is the constant that comes before a variable (or variables).

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    $\begingroup$ Moreover, calling a coefficient a constant unnecessarily complicates things: in the family of curves $y=px^2+qx+3,$ the coefficents $p$ and $q$ are constants within each curve but vary across curves, that is, they are arbitrary constants, which means that they can also be considered variables. $\endgroup$
    – ryang
    Aug 5 at 7:39
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    $\begingroup$ I'd call your p and q parameters, rather than constants or variables. Again, that conveys more meaning. $\endgroup$
    – Sue VanHattum
    Aug 5 at 17:15
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    $\begingroup$ In point #3, and the blue links within, here, and in the side note here, I too called the above $p$ a parameter, and pointed out that "arbitrary constant" and "arbitrary variable" are, amusingly, synonyms. A parameter is a specific type of arbitrary constant. $\endgroup$
    – ryang
    Aug 5 at 17:26
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It depends on the context. For example, in physics we often represent constants with letters. For example, the equation for gravitational force between two masses ($m_1$and $m_2$) separated by a distance $r$ is given by $F = G(m_1m_2/r^2)$ where G is a constant.

But in mathematics we might write $y = ax^2 + bx + c$ where $a$, $b$, and $c$ are constants, but we call them coefficients.

So, what is the difference? The difference is that in the physics expression G stands for a known value, $6.6743 x 10^-11 m^3/kgs^2$, but in the math example, the coefficients are arbitrary and unspecified. They are constants in that they do not change like x and y, but arbitrary in that we haven't assigned a specific value to them.

In the sense of how they operate, coefficients are constants. Whether we call them constants or coefficients depends on whether we've actually actually assigned a value to them.

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