Intermediate Algebra (11th edition)

CHAPTER 5 Review Exercises 311

5.5 Dividing Polynomials

Dividing by a Monomial
To divide a polynomial by a monomial, divide each term
in the polynomial by the monomial, and then write each
fraction in lowest terms.

Dividing by a Polynomial
Use the “long division” process. The process ends when
the remainder is 0 or when the degree of the remainder is
less than the degree of the divisor.

Divide.

1 Remainder

4 m+ 4

4 m+ 5

• 2 m^2 - 2 m


• 2 m^2 + 2 m

m^3 +m^2

m+ 1  m^3 - m^2 + 2 m+ 5

m^2 - 2 m+ 4

m^3 - m^2 + 2 m+ 5

m+ 1

=x^2 - 2 x+ 3 -

4

x

=

2 x^3

2 x

-

4 x^2

2 x

+

6 x

2 x

-

8

2 x

2 x^3 - 4 x^2 + 6 x- 8

2 x

The answer is

m^2 - 2 m+ 4 +

1

m+ 1

.

CONCEPTS EXAMPLES

Dividing Functions

If and define functions, then

a

ƒ

g

b1x 2 

ƒ 1 x 2

g 1 x 2

, g 1 x 2 0.

ƒ 1 x 2 g 1 x 2 Let and

a

ƒ

g

b1x 2 =

ƒ 1 x 2

g 1 x 2

=

x^2

2 x+ 1

, xZ-

1

2

ƒ 1 x 2 =x^2 g 1 x 2 = 2 x+1.

REVIEW EXERCISES

CHAPTER 5

5.1 Simplify. Write answers with only positive exponents. Assume that all variables

represent nonzero real numbers.

1. 
   
   
   
   2. 
      
      
      
      3. 
         
      
      
      
      
   
   
   
   

4. 5. 6.

7. 8. 9.

10. 11. 12.

13. 14. 15.

16. 17. 18.

19. 20. 21.

15 p-^2 q 214 p^5 q-^32

2 p-^5 q^5

6 m-^4 n^3

• 3 mn^2

1 - 3 x^4 y^3214 x-^2 y^52

a

3 r^5

5 r-^3

b

• 2
  a

9 r-^1

2 r-^5

b

3

a

6 m-^4

m-^9

b

• 1
  a

m-^2

16

a b

5 z-^3

z-^1

b

5

z^2

13 r 22 r^4

r-^2 r-^3

1 z-^323 z-^615 m-^3221 m^42 -^319 r-^32 -^2

13 -^4221 x-^42 -^21 xy-^32 -^2

5 -^1 - 6 -^12 -^1 + 4 -^1 - 30 + 30

a

5

4

b

• 2
  a

2

3

b

2 -^4

1 - 32 -^2

a 1 - 523

1

3

b

4

43