Intermediate Algebra (11th edition)

EXERCISES 33–38

FOR INDIVIDUAL OR GROUP WORK

We can show a connection between dividing one polynomial by another and factoring

the first polynomial. Let Work Exercises 33–38 in order.

33.Factor 34.Solve

35.Evaluate. 36.Evaluate

37.Complete the following sentence: If then is a factor of

38.Use the conclusion reached in Exercise 37to decide whether is a factor of

Q 1 x 2 = 3 x^3 - 4 x^2 - 17 x+6.Factor completely.Q 1 x 2

x- 3

P 1 a 2 =0, x- P 1 x 2.

P 1 - 42 PA 23 B.

P 1 x 2. P 1 x 2 =0.

P 1 x 2 = 2 x^2 + 5 x-12.

RELATING CONCEPTS

726 APPENDIX B Synthetic Division

EXERCISES

Use synthetic division to find each quotient. See Examples 1 and 2.

4. 5. 6.

7. 8.

9. 10.

11.

12.

13.

14.

15.

16.

Use the remainder theorem to find See Example 3.

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    22. 23.Explain why a 0 remainder in synthetic division of by indicates that kis a solu-
        tion of the equation
        24.Explain why it is important to insert 0s as placeholders for missing terms before perform-
        ing synthetic division.
    
    
    
    

Use synthetic division to decide whether the given number is a solution of the equation. See

Example 4.

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    30. 
        
    
    
    
    


28. 
    

    32.x^4 - x^3 - 6 x^2 + 5 x+ 10 =0; x=- 2

    
    

x^4 + 2 x^3 - 3 x^2 + 8 x- 8 =0; x=- 2

2 x^3 - x^2 - 13 x+ 24 =0; x=- 3 5 x^3 + 22 x^2 +x- 28 =0; x=- 4

3 x^3 + 2 x^2 - 2 x+ 11 =0; x=- 2 3 x^3 + 10 x^2 + 3 x- 9 =0; x=- 2

x^3 - 2 x^2 - 3 x+ 10 =0; x=- 2 x^3 - 3 x^2 - x+ 10 =0; x=- 2

P 1 x 2 =0.

P 1 x 2 x-k

P 1 x 2 = 2 x^3 - 4 x^2 + 5 x-33; k= 3 P 1 x 2 =x^3 - 3 x^2 + 4 x-4; k= 2

P 1 x 2 =-x^3 - 5 x^2 - 4 x-2; k=- 4 P 1 x 2 =-x^3 + 5 x^2 - 3 x+4; k= 3

P 1 x 2 = 2 x^3 - 4 x^2 + 5 x-3; k= 2 P 1 x 2 =x^3 + 3 x^2 - x+5; k=- 1

P 1 k 2.

1 m^6 + 2 m^4 - 5 m+ 112 , 1 m- 22

1 - 3 y^5 + 2 y^4 - 5 y^3 - 6 y^2 - 12 , 1 y+ 22

12 t^6 - 3 t^5 + 2 t^4 - 5 t^3 + 6 t^2 - 3 t- 22 , 1 t- 22

1 - 4 r^6 - 3 r^5 - 3 r^4 + 5 r^3 - 6 r^2 + 3 r+ 32 , 1 r- 12

12 y^5 - 5 y^4 - 3 y^2 - 6 y- 232 , 1 y- 32

1 x^5 - 2 x^3 + 3 x^2 - 4 x- 22 , 1 x- 22

5 p^3 - 6 p^2 + 3 p+ 14

p+ 1

4 a^3 - 3 a^2 + 2 a- 3

a- 1

1 p^2 - 3 p+ 52 , 1 p+ 12 1 z^2 + 4 z- 62 , 1 z- 52

4 y^2 - 5 y- 20

y- 4

2 a^2 + 8 a+ 13

a+ 2

3 x^2 - 5 x- 12

x- 3

4 m^2 + 19 m- 5

m+ 5

x^2 - 4 x- 21

x+ 3

x^2 - 6 x+ 5

x- 1