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## IDENTIFYING VARIABLE PARTS AND COEFFICIENTS OF TERMS

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The concepts for this exercise are summarized below. For a complete discussion, read the 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.

In the term  4xy , the coefficient is  4  and the variable part is  xy .

In the term  -7x2y3 , the coefficient is  -7  and the variable part is  x2y3 .

If you don't "see" a coefficient, then it is  1 .
That is,  x = (1)x  has coefficient  1 .
Also,  x2y3 = (1)x2y3  has coefficient  1 .
It's never necessary to write a coefficient of  1 , because multiplication by  1  doesn't change anything.

In the term  -x , the coefficient is  -1 , because  -x = (-1)x .
In the term  -x2y , the coefficient is  -1 , because  -x2y = (-1)x2y .

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  1/2 ,  the square root of  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 .
You should write  x2yz , not  yx2z  or  yzx2 .

EXAMPLE:
The user input is in bold.
When reporting the variable part, variables must be written in alphabetical order.

Consider the term  y(3)(2x)(-1) .
What is the numerical coefficient?   Answer: -6
What is the variable part?   Answer: xy
Write the term in the most conventional way:   Answer: -6xy
Click on "new problem" to get started!

Consider the term:

What is the numerical coefficient?

What is the variable part?

Write the term in the most conventional way:

When you're ready to time yourself, use these buttons.
When you "end timing," you'll get a summary sheet of your results. Good luck!