Use the rational zeros theorem to write a list of all possible rational zeros of the function. f(x) = 3x3 + 39x2 + 39x + 27

First, we can factor this to make it easier to solve:

3(x^3 + 13x^2 + 13x + 9)

Now, we can use the rational root theorem like so:

List factors of 9:

1, 3, 9.

List factors of 1:

1

Because of this, we know our possible rational roots are:

+/-1, +/-3, +/-9

If none of these zeros fit using the remainder theorem, then we know our roots will be irrational.

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068