Basic Mathematics for College Students

Addition symbols separate expressions into parts called terms.For example, the

expression x+ 8 has two terms.

8

First term Second term

Since subtraction can be written as addition of the opposite, the expression

has three terms.

First term Second term Third term

In general, a termis a product or quotient of numbers and/or variables. A single

number or variable is also a term. Examples of terms are:

4, , , , , ,

Caution! By the commutative property of multiplication, and

. However, when writing terms, we usually write the
numerical factor first and the variable factors in alphabetical order.

The numerical factor of a term is called the coefficientof the term. For instance,

the term has a coefficient of 6 because. The coefficient of is

because. More examples are shown below.

A term such as 4, that consists of a single number, is called a constant term.

This term could be written.

Because

Because

Because

The coefficient of a constant term is that constant.

The Language of Algebra Terms such as and have impliedcoefficients of 1.

Impliedmeans suggested without being precisely expressed.

x y

t 1 t

x 1 x

 6 x^16 x 61 x

34 b

 15 ab^2  15 ab^2

6 r 6 r 6 r  15 ab^2  15

 15 b^2 a 15 ab^2

r 6  6 r

 15 ab^2

3

n

y 6 r w^3 3.7x^5

a^2  3 a 9  a^2  ( 3 a)  (9)

a^2  3 a 9

x 

640 Chapter 8 An Introduction to Algebra

Term Coefficient

8

1

27 27

t  1

x

x 6 ^16

3

4

3

4 b

0.9pq 0.9

8 y^2

EXAMPLE (^1) Identify the coefficient of each term in the expression:
StrategyWe will begin by writing the subtraction as addition of the opposite.
Then we will determine the numerical factor of each term.
WHYAddition symbols separate expressions into terms.
SolutionIf we write as , we see that it has three terms:
, , and 6. The numerical factor of each term is its coefficient.
The coefficient of is because means.
The coefficient of is because means.
The coefficient of the constant 6 is 6.
x  1 x  1 x
7 x^277 x^27 x^2
7 x^2 x
7 x^2 x 6 7 x^2 (x) 6
7 x^2 x 6
Self Check 1
Identify the coefficient of each
term in the expression:
Now TryProblem 23
p^3  12 p^2  3 p 4