Algebra 2H A
Chapter 5 Review
Name:_________________________________
Write each polynomial in standard form. Then classify it by degree and by number of terms.
1. 4x + x + 2
2. 3 + 3x2  3x
3. 6x4  1
4. 5m3  3m3
Determine the end behavior of the graph of each polynomial function.
5. y = 3x4 + 6x3  x2 + 12
6. y = 50  3x3 + 5x2
7. y = 2x5 + x2  4
8. y = 5 + 2x + 7x2  5x3
9. y = 20  5x6 + 3x  11x3
10. y = 6x + 25 + 4x3  x2
Find the zeros of each function. Then graph the function.
11. y = (x + 1)(x  1)(x  3)
12. y = (x + 2)(x  3)
13. y = x(x  2)(x + 5)
Find the zeros of each function. State the multiplicity of multiple zeros.
14. y = (x  5)3
15. y = x(x  8)2
16. y = (x  2)(x + 7)3
Find the real or imaginary solutions of each equation by factoring.
17. 8x3  27 = 0
18. x3 + 64 = 0
19. x4  9x2 + 14 = 0
20. x4 + 13x2 + 36 = 0
21. x3  5x2 + 4x = 0
22. x3  81x = 0
Divide using long division.
23. (x2  13x – 48) ÷ (x + 3)
24. (3x3  x2  7x + 6) ÷ (x + 2)
Divide using synthetic division.
25. (x3  8x2 + 17x  10) ÷ (x  5)
26. (x3 + 5x2  x  9) ÷ (x + 2)
27. (2x3 + 15x2  15) ÷ (x  3)
28. (7x3 + 15x + 9) ÷ (x + 1)
Use synthetic division and the given factor to completely factor each polynomial function.
29. y = x3 + 3x2  13x  15; (x + 5)
30. y = x3  3x2  10x + 24; (x  2)
Use synthetic division and the Remainder Theorem to find P(a).
31. P(x) = 5x3  12x2 + 2x + 1, a = 3
32. P(x) = 2x3  4x2 + 3x  6, a = 2
Write a polynomial function with rational coefficients so that P(x) = 0 has the given roots.
33. 4 and 6
34. 5 , 1, and 1
35. 5 and 3i
36. 5i and i
Find all roots for P(x) = 0.
37. P(x) = x3  5x2 + 2x + 8
38. P(x) = x3 + x2  17x + 15
39. P(x) = 2x3 + 13x2 + 17x  12
40. P(x) = x3 + 4x2 +4x +16
41. P(x) = x 4 6x3 + 9x2  6x +8
42. P(x) = x 4 18x2 +32
Expand each binomial.
43. (x + 2y)4
44. (3 + d)5
45. (2x  3)3
46. (x  1)6
Find a polynomial function that best models each set of values.
47.The table shows the annual population of Florida for selected years.
Year
Population (millions)
1970
1980
1990
2000
6.79
9.75
12.94
15.98
48.
Determine the cubic function that is obtained from the parent function y = x3 after each sequence of
transformations.
49. a vertical stretch by a factor of 2, a vertical translation 5 units down; and a horizontal translation 3 units left
50. a reflection across the x-axis; a vertical translation 6 units up; and a horizontal translation 4 units right
51. a vertical stretch by a factor of 3; a reflection across the x-axis; and a horizontal translation 6 units left
1
; a reflection across the x-axis; and a vertical translation 5 units down and a
2
horizontal translation 2 units left
52. a vertical stretch by a factor of
53. a vertical stretch by a factor of 2; a reflection across the y-axis; a vertical translation 2 units down