Algebra II Honors
Chapter 5A
Name _________________
5.1 Write each polynomial in standard form. Then classify it by degree and by number of terms.
1. 4x + x + 2
2. 3 + 3x  3x
3. 6x4  1
4. 1  2s + 5s4
5. x2 + 3x  4x3
6. a3(a2 + a + 1)
7. x(x + 5)  5(x + 5)
8. p(p  5) + 6
9. (3c2)2
Determine the end behavior of the graph of each polynomial function.
10. y = 3x4 + 6x3  x2 + 12
11. y = 50  3x3 + 5x2
12. y = x + x2 + 2
13. y = 4x2 + 9  5x4  x3
14. y = 12x4  x + 3x7  1
15. y = 2x5 + x2  4
Determine the degree of the polynomial function with the given data.
16.
17.
18. Error Analysis A student claims the function y = 3x4  x3 + 7 is a fourth-degree polynomial with end
behavior of down and down. Describe the error the student made. What is wrong with this statement?
19. Writing Explain why finding the degree of a polynomial is easier when the polynomial is written
in standard form.
5.2 Write each polynomial in factored form. Check by multiplication.
20. 2x3 + 10x2 + 12x
21. x4  x3  6x2
22. 3x3 + 18x2  27x
23. x3  2x2 + x
Find the zeros of each function. Then graph the function.
24. y = (x + 1)(x  1)(x  3)
25. y = (x + 2)(x  3)
26. y = x(x  2)(x + 5)
27. y = (x + 4)2(x + 1)
Write a polynomial function in standard form with the given zeros.
28. x = 1, 3, 4
29. x = 1, 1, 2
30. x = 4, 2, 3, 0
31. x = 3, 0, 0, 5
Find the zeros of each function. State the multiplicity of multiple zeros.
32. y = (x  5)3
33. y = x(x  8)2
34. y = (x  2)(x + 7)3
35. y = (2x + 5)(x  3)2
36. The side of a cube measures 3x + 2 units long. Express the volume of the cube as a
polynomial.
Algebra II Honors
Chapter 5A
Name _________________
5.3 Find the real or imaginary solutions of each equation by factoring.
37. 8x3  27 = 0
38. x3 + 64 = 0
39. 2x3 + 54 = 0
40. 2x3  250 = 0
41. 4x3  32 = 0
42. 27x3 + 1 = 0
43. 64x3  1 = 0
44. x3  27 = 0
45. x4  5x2 + 4 = 0
46. x4  12x2 + 11 = 0
47. x4  10x2 + 16 = 0
48. x4  8x2 + 16 = 0
49. x4  9x2 + 14 = 0
50. x4 + 13x2 + 36 = 0
51. x4  10x2 + 9 = 0
52. x4 + 3x2  4 = 0
53. Error Analysis Your friend claims that the zeros of 3x3 + 7x2  22x  8 = 0 are 4, 2, and 1. What did your
friend do wrong? What are the correct factors?
54. Your mother is 25 years older than you. Your father is 3 years older than your mother. The product of all
three ages is 32,130. How old is your father?