Beginning Algebra, 11th Edition

320 CHAPTER 5 Exponents and Polynomials

OBJECTIVES

Adding and Subtracting Polynomials;

Graphing Simple Polynomials

5.4

1 Identify terms and

coefficients.

2 Add like terms.

3 Know the

vocabulary for

polynomials.

4 Evaluate

polynomials.

5 Add and subtract

polynomials.

6 Graph equations

defined by

polynomials of

degree 2.

OBJECTIVE 1 Identify terms and coefficients. In an expression such as

the quantities 5 x, and 8 are called terms.(See Section 1.8.) In the first (or

leading) term the number 4 is called the numerical coefficient,or simply the

coefficient,of In the same way, 6 is the coefficient of in the term and 5 is

the coefficient of xin the term 5 x. The constant term 8 can be thought of as

since so 8 is the coefficient in the term 8.

Identifying Coefficients

Name the coefficient of each term in these expressions.

(a) can be written as

The coefficients

are 1 and.

(b) can be written as

The coefficients

are 5 and. NOW TRY

OBJECTIVE 2 Add like terms.Recall from Section 1.8that like termshave

exactly the same combination of variables, with the same exponents on the variables.

Only the coefficients may differ.

and

and

and

and

Using the distributive property, we combine, or add, like terms by adding their

coefficients.

2 xy^2 - xy^2

3 pq - 2 pq

6 y^9 , - 37 y^9 , y^9

19 m^514 m^5

• 1

5 - v^35 v^0 + 1 - 1 v^32.

• 6

x- 6 x^41 x+ 1 - 6 x^42.

EXAMPLE 1

8 # 1 = 8 x^0 , x^0 = 1,

x^3. x^26 x^2 ,

4 x^3 ,

4 x^3 , 6 x^2 ,

4 x^3 + 6 x^2 + 5 x+8,

⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩

⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩

7 x and 7 y

and z

2 pq and 2 p

- 4 xy^2 and 5 x^2 y

z^4 Examples

of

unlike terms

NOW TRY
EXERCISE 1
Name the coefficient of each
term in the expression.

t- 10 t^2

NOW TRY
EXERCISE 2
Simplify by adding like
terms.

NOW TRY ANSWERS

1. 1;


2. 2 x^2 + 2 x
   
   
   • 10
   
   
   
   

3 x^2 - x^2 + 2 x

Adding Like Terms

Simplify by adding like terms.

(a)

Distributive property

= 2 x^3 Add.

= 1 - 4 + 62 x^3

- 4 x^3 + 6 x^3

EXAMPLE 2

(b)

=- 4 x^6

= 19 - 14 + 12 x^6 x^6 = 1 x^6

9 x^6 - 14 x^6 +x^6

(c)

= 16 m^2 + 5 m

= 112 + 42 m^2 + 5 m

12 m^2 + 5 m+ 4 m^2 (d)

NOW TRY

= 6 x^2 y

= 13 + 4 - 12 x^2 y

3 x^2 y+ 4 x^2 y-x^2 y

Examples

of

like terms

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