College Algebra, 2013a

280 Polynomial Functions
3.3.3 Exercises
In Exercises 1 - 10, for the given polynomial:
ˆ Use Cauchy’s Bound to find an interval containing all of the real zeros.
ˆ Use the Rational Zeros Theorem to make a list of possible rational zeros.
ˆ Use Descartes’ Rule of Signs to list the possible number of positive and negative real zeros,
counting multiplicities.
1. f(x) =x 3 − 2x 2 − 5x +6 2. f(x) =x 4 +2x 3 − 12x 2 − 40x − 32
3. f(x) =x 4 − 9x 2 − 4x +12 4. f(x) =x 3 +4x 2 − 11x +6
5. f(x) =x 3 − 7x 2 + x − 7 6. f(x) =−2x 3 +19x 2 − 49x +20
7. f(x) =−17x 3 +5x 2 +34x − 10 8. f(x) =36x 4 − 12x 3 − 11x 2 +2x +1
9. f(x) =3x 3 +3x 2 − 11x − 10 10. f(x) =2x 4 + x 3 − 7x 2 − 3x +3
In Exercises 11 - 30, find the real zeros of the polynomial using the techniques specified by your
instructor. State the multiplicity of each real zero.
11. f(x) =x 3 − 2x 2 − 5x + 6 12. f(x) =x 4 +2x 3 − 12x 2 − 40x − 32
13. f(x) =x 4 − 9x 2 − 4x + 12 14. f(x) =x 3 +4x 2 − 11x +6
15. f(x) =x 3 − 7x 2 + x − 7 16. f(x) =−2x 3 +19x 2 − 49x +20
17. f(x) =−17x 3 +5x 2 +34x − 10 18. f(x) =36x 4 − 12x 3 − 11x 2 +2x +1
19. f(x) =3x 3 +3x 2 − 11x − 10 20. f(x) =2x 4 + x 3 − 7x 2 − 3x +3
21. f(x) =9x 3 − 5x 2 − x 22. f(x) =6x 4 − 5x 3 − 9x 2
23. f(x) =x 4 +2x 2 − 15 24. f(x) =x 4 − 9x 2 +14
25. f(x) =3x 4 − 14x 2 − 5 26. f(x) =2x 4 − 7x 2 +6
27. f(x) =x 6 − 3x 3 − 10 28. f(x) =2x 6 − 9x 3 +10
29. f(x) =x 5 − 2x 4 − 4x + 8 30. f(x) =2x 5 +3x 4 − 18x − 27