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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).