4.  x = -1, 0 , 1
 x = -2, 0, 2
 x = -2, -1, 1, 2

5. x = -2, 0, 2 x = -2, -1, 1, 2 x = -1, 0 , 1

6.  a < 0; x = 2, -1

7.  -(x – 2) (x + 1)

8.  a < 0; x = 2, -1, 3 5
 a > 0; x = 0, 6 (double root), 2i

9. 4 3 2
x 7 x 8x 8x 8

10. 5 4 3 2
x 12x 40x 48x 144x

11.  x = 2 (double root) 5
 x = 0 (triple root), 2, -3
 x= 6 3

12.  .
f ( x) x 4
4x 3
x 2
20 x 20

13.  . ( x)
f x 5
x 4
6x 3

14.  . ( x)
f x 2
12 x 33

15. (7 + 5i) + (-4 + 2i)

16. 3+ 7i

17. (2 - 6i) – (-3 + i)

18. 5 – 7i

19. (1 – 5i)(3 – 2i)

20. -7 – 17i

21. _
6 i
4 i

22. 6 i 4 i
4 i 4 i
2
24 6i 4i i
2
16 4i 4i i
24 6i 4i 1
16 4i 4i 1
23 10i
17

23. 4 2
 .
f ( x) x 4x 5

24.  x = ± i 5, x 1

25.  .
f ( x) 4x 3
4x 2
15 x

26.  x = 0, x = -3/2, x = 5/2

27. 3 2
 .
f ( x) 2x 13x 13x 3

28.  P/q : ±1, ±3, ±1/2, ±3/2
1 7 61
x= , x
2 2

29.  .
f ( x) x 4
6x 3
x 2
54 x 72

30.  p/q =
±1, ±2, ±3, ±4, ±6, ±8, ±9, ±12, ±18, ±24, ±36
, ±72
 x = -2, x = -4, x = -3, x = 3

31. 3 2
 .
f ( x) 2x x 25 x 12

32.  p/q = ±1, ±2, ±3, ±4, ±6, ±12, ±1/2, ±3/2
 x = 3, x = ½, x = -4

33. 3 2
 .
f ( x) 2x 5x 9x 8

34.  x = -1.661, x = .695, x = 3.465

35. .
 f ( x) x5 3x 4 13x3 39 x 2 36 x 108, ( x 3)

36. ( x 3)( x 3)( x 2)( x 2)( x 3)