Identifying Variable Parts and Coefficients of Terms
Numerical Coefficients and Variable Parts
In a term like there are two parts that are usually of interest: the numerical part () and the variable part () .
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 the coefficient is and the variable part is
In the term the coefficient is and the variable part is
Coefficients and
If you don't ‘see’ a coefficient, then it is That is, has coefficient Also, has coefficient It's never necessary to write a coefficient of because multiplication by doesn't change anything.
In the term the coefficient is because In the term the coefficient is because
Constant Terms
A term like 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 and are all constant terms.
Conventional Way to Write Terms
In any term, it is conventional to write the numerical coefficient first. Thus, you should write not or
Also, it is conventional to write any variable(s) in alphabetical order. Thus, you usually want to write not Similarly, write not or
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Example
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.
Consider the term
What is the numerical coefficient? Answer:
What is the variable part? Answer:
Write the term in the most conventional way: Answer:
Practice
When reporting the variable part, variables must be written in alphabetical order.