Unit 6 Review - Polynomials

advertisement
Name:____________________
ALGEBRA II POLYNOMIAL REVIEW
1. Sketch a graph of a polynomial that has one double root.
2. Sketch a graph of a polynomial that has three double roots.
3. Solve for all complex solutions, answers must be in exact, radical form. 0 = x4 +5x2 –36
4. Solve for all complex solutions, answers must be in exact, radical form. 0 = x4 –10x2 +16
5. Solve for all complex solutions: 0 = 2x3 + 10x2–3x –15.
6. Solve for all complex solutions: 0 = 4x4 + 7x3 + 4x + 7.
7. What are the possible rational zeros for 4x3 – 17x2 – 5x + 10?
8. What are the possible rational zeros for 4x4 + 7x3 + 4x + 7?
9. One zero of f(x) = x4 – 9x3 +9x2 – 81x is –3i. What are the other zeros of this function?
10. One zero of f(x) = x3 – 4x2 + 16x–64 is 4i. What are the other zeros of this function?
11. Determine the remainder of the function f(x) = 2x2 + x – 4 when it is divided by x + 2.
12. Determine the remainder of the function f(x) = x4 – x2 + 2x – 7 when it is divided by x– 1.
13. The polynomial 4x2+3x – 10 = 0 has 2 real solutions. One of the solutions is an integer but
the other is not. The noninteger solution is between which 2 consecutive integers?
14. The polynomial 2x3 + 11x2 – 8x –44 = 0 has 3 real solutions. Two of the solutions are
integers but the other is not. The noninteger solution is between which 2 consecutive integers?
15. P(x)= 3 − 8. What are the nature of the roots of P(x)?
16. P(x)= x4 +5x2 –36. What are the nature of the roots of P(x)?
17. What is the completely factored form of this expression? x3 +3x2 – 10x + 24
18. What is the completely factored form of this expression? x3 – 4x2 – 25x + 100
19. P(x)= x3 – 4x2 – 25x + 100 and P(4)=0. Name a factor of P(x).
20. P(x)= x4 –14x2 +45 and P(3)=0. Name a factor of P(x).
21. Write a polynomial in standard form with roots x = 4, 3, 0.
22. Write a polynomial in standard form with roots x = 1, 5, -1.
23. Factor f(x) = x3 + 8
24. Factor f(x) = 8x3 – 27
25. G(x) = 7x3 – 4x + 2. What is the relative minimum and relative maximum of G(x)?
Determine the end behavior of G(x).
26.G(x)= x4 –10x2 +16. What is the relative minimum and relative maximum of G(x)?
Determine the end behavior of G(x).
Download
Related flashcards

Algebra

20 cards

Polynomials

21 cards

Abstract algebra

19 cards

Category theory

14 cards

Create Flashcards