Fundamentals of Mathematics, 2008a

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Rather than rewriting the expression when a subtraction occurs, we can identify terms more quickly
by associating the + or - sign with the individual quantity.
Example 11.3
a + 7 − b − m. Associating the sign with the individual quantities, we see that this expression
consists of the four terms a, 7, −b, −m.
Example 11.4
5m − 8n. This expression consists of the two terms, 5m and −8n. Notice that the term 5m is
composed of the two factors 5 and m. The term −8n is composed of the two factors −8 and n.
Example 11.5
3x. This expression consists of one term. Notice that 3x can be expressed as 3x + 0 or 3x ·
1 (indicating the connecting signs of arithmetic). Note that no operation sign is necessary for
multiplication.
11.2.3.2 Practice Set A
Specify the terms in each expression.
Exercise 11.2.1 (Solution on p. 682.)
x + 7
Exercise 11.2.2 (Solution on p. 682.)
3m − 6n
Exercise 11.2.3 (Solution on p. 682.)
5y
Exercise 11.2.4 (Solution on p. 682.)
a + 2b − c
Exercise 11.2.5 (Solution on p. 682.)
−3x − 5
11.2.4 Coecients
We know that multiplication is a description of repeated addition. For example,
5 · 7 describes 7 + 7 + 7 + 7 + 7
Suppose some quantity is represented by the letter x. The multiplication 5x describes x + x + x + x + x. It
is now easy to see that 5x species 5 of the quantities represented by x. In the expression 5x, 5 is called the
numerical coecient, or more simply, the coecient of x.
Coecient
The coecient of a quantity records how many of that quantity there are.
Since constants alone do not record the number of some quantity, they are not usually considered as numerical
coecients. For example, in the expression 7x + 2y − 8z + 12, the coecient of
7x is 7. (There are 7 x's.)
2y is 2. (There are 2 y 's.)
−8z is −8. (There are −8z 's.)
The constant 12 is not considered a numerical coecient.
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