LESSON READ-THROUGH
by Dr. Carol JVF Burns (website creator)
Follow along with the highlighted text while you listen!

• PRACTICE (online exercises and printable worksheets)
• This page gives an in-a-nutshell discussion of the concepts.
  Want more details, more exercises? Read the full text!

In a term like $\,2x\,$, there are two parts that are usually of interest:
the numerical part ($\,2\,$) and the variable part ($\,x\,$) .

The numerical part is given a special name—it is called
the numerical coefficient or, more simply, the coefficient of the term.

If you don't ‘see’ a coefficient, then it is $\,1\,$.
That is, $\,x = (1)x\,$ has coefficient $\,1\,$.
Also, $\,x^2y^3 = (1)x^2y^3\,$ has coefficient $\,1\,$.
It's never necessary to write a coefficient of $\,1\,$, because multiplication by $\,1\,$ doesn't change anything.

A term like $\,2\,$ that has no variable part is called a constant term,
because it is constant—it never changes.
It has no variable part that can ‘hold’ different values.
Thus $\,\frac{1}{2}\,$, $\,\sqrt{3}\,$, and $\,9.4\,$ are all constant terms.

In any term, it is conventional to write the numerical coefficient first.
Thus, you should write $\,4xy\,$, not $\,xy4\,$ or $\,x4y\,$.

Also, it is conventional to write any variable(s) in alphabetical order.
Thus, you usually want to write $\,5xy\,$, not $\,5yx\,$. Similarly, write $\,x^2yz\,$, not $\,yx^2z\,$ or $\,yzx^2\,$.

For this web exercise, when reporting the variable part, variables must be written in alphabetical order.
The user input is in bold in the example below.