Identifying Variable Parts and Coefficients of Terms

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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 Back to the Table of Contents

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