Polynomial Functions Worksheet With Answer Key Page 11
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17Advanced Algebra Honors
Wkst 6-6: The Fundamental Theorem of Algebra
Find all the zeros of each function.
3
3
1. y = 5x
− 5x
2. f(x) = x
− 16x
3
2
3
2
3. g(x) = 12x
− 2x
− 2x
4. y = 6x
+ x
− x
3
2
3
5. f(x) = 5x
+ 6x
+ x
6. y = −4x
+ 100x
For each equation, state the number of complex roots, the possible number of real roots,
and the possible rational roots.
2
2
7. 2x
+ 5x + 3 = 0
8. 3x
+ 11x − 10 = 0
4
2
3
9. 2x
− 18x
+ 5 = 0
10. 4x
− 12x + 9 = 0
5
3
2
11. 6x
− 28x + 15 = 0
12. x
− 2x + 7 = 0
− x
3
2
4
2
13. x
− 6x
− 7x − 12 = 0
14. 2x
+ x
− x + 6 = 0
5
4
3
2
6
4
2
15. 4x
− 5x
+ x
− 2x
+ 2x − 6 = 0
16. 7x
+ 3x
− 9x
+ 18 = 0
2
3
4
5
3
3
4
5
17. 5 + x + x
+ x
+ x
+ x
= 0
18. 6 − x + 2x
− x
+ x
− 8x
= 0
Find all the zeros of each function.
3
2
3
2
19. f(x) = x
− 9x
+ 27x − 27
20. y = 2x
− 8x
+ 18x − 72
3
3
2
21. y = x
− 10x − 12
22. y = x
− 4x
+ 8
3
3
2
23. f(x) = 2x
+ x − 3
24. y = x
− 2x
− 11x + 12
3
2
3
2
25. g(x) = x
26. f(x) = x
+ 4x
+ 7x + 28
+ 3x
+ 6x + 4
4
2
4
2
27. g(x) = x
− 5x
− 36
28. y = x
− 7x
+ 12
4
2
4
2
29. y = 9x
+ 5x
− 4
30. y = 4x
− 11x
− 3
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