Fundamental Theorem of Algebra Worksheet



Fundamental Theorem of Algebra/Remainder Theorem Name: ______________________

Date: _____________

Use the graph to write the equation in factored form.

1. [pic]2. [pic]

3. [pic]

4. [pic]

Write the equation in factored form given the following:

5. zeros: 3, -5

degree: 3

3 has a multiplicity of 2.

6. zeros: 0, -2, 4

degree: 5

0 has a multiplicity of 3.

7. zeros: 7/2, -3, 8

degree: 3

8. zeros: -1, 2

degree: 4

-1 has a multiplicity of 3.

Use the Remainder Theorem to find the remainder when f(x) is divided by x-c. Then use the Factor Theorem to determine whether x-c is a factor of f(x).

If so, write f(x) in factored form [f(x) = (x-c)(quotient)]

9. f(x) = 4x3 –3x2 – 8x + 4 ;

x – 2

10. f(x) = –4x3 + 5x2 + 8 ;

x + 3

11. f(x) = 3x4 – 6x3 – 5x + 10;

x – 2

12. f(x) = 3x6 + 82x3 + 27 ;

x + 3

13. f(x) = 4x6–64x4+x2–15;

x + 4

14. f(x) = x6–16x4+x2–16 ;

x + 4

Vocabulary Check:

15. If 6 is a zero of the function f, then f(6) = _____.

16. If -2 is a solution to the equation g(x) = 0, then g(-2) = _____.

17. If 3 is a zero of the polynomial f(x), then x-3 is called a _____ of f(x).

18. If f(8) = 0, then _____ is an x-intercept point of the graph of f.

19. If x + 3 is a factor of the polynomial h(x), then _____ is a zero or solution.

20. If 2 is an x-intercept of the graph of polynomial f(x), then _____ is a factor of f(x).

21. If x-6 is a factor of the polynomial g(x), then g (_____) = 0

22. The degree of polynomial x3 – 2x4 + 5x2 + x – 3 is _____.

23. If the solution set to f(x) = 0 is {5, 3i, -3i}, then an x-intercept point of the graph is _____.

24. Using the Remainder Theorem, if the polynomial f(x) is divided by x + 7 and the remainder is 5, then f(-7) = _____.

25. Using the Remainder Theorem, if the polynomial g(x) is divided by x – 3, and the remainder is 0, then g(_____) = _____. Also, x – 3 is a _____ of g(x).

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