Polynomials Review
Name_______________________
Write each polynomial in standard form. Then classify it by degree and by number of terms.
1
 5x
3
1. a2  4a  5a2  a
2. 3x 
4. 15  y 2  10 y  8  8 y
5. 6c – 4c+ 7 – 8c
3. 3n + n – n – 3 – 3n
2
2
2
3
6. 3x2  5x  x2  x  4 x
Determine the end behavior of the graph of each polynomial function.
8. y = -x – 2x
3
10. y 
1 4
1
x  5x2 
2
2
9. y = 7x + 3x – 2x
5
3
12. y = –x + 6x – 36
12
6
Write each polynomial in factored form.
13. x
3
+ 5x
3
14. x + x
2
– 6x
Write a polynomial function in Factored form with the given zeros.
16. x = 3, 2, 1
17. x= 1, 1, 2
18. x = 2, 1, 1
19. x = 1, 2, 6
20. x = 3, 1, 5
21. x = 0, 0, 2, 3
Find the zeros of each function. State the multiplicity of multiple zeros.
22. y = (x  2)(x + 4)
23. y = (x  7)(x  3)
24. y = (x + 1)(x  8)(x  9)
25. y = x (x + 1)(x + 5)
2
26. y = x
(x + 1)
3
27. y = (x  3)(x  4)
2
Find the real or imaginary solutions of each equation by factoring.
3
28. x + 27 = 0
30. 9 = 4x  16
2
2
29. x + 400 = 40x
Solve each equation.
35. t  3t  10t = 0
3
2
37. t  6t + 12t  8 = 0
3
2
Determine whether each of the following is a factor of x 3  5x 2  2x + 24.
41. x  3
40. x + 2
42. x + 4
Divide.
43. (x  3x + 2) ÷ (x  1)
3
2
44. (x  x  6x) ÷ (x  3)
3
2
45. (2x + 10x + 8x) ÷ (x + 4)
46. (x + x  6) ÷ (x + 3)
47. (x  4x + 2) ÷ (x  2)
48. (x + 11x + 12) ÷ (x + 3)
3
2
2
4
2
2
3
Find the roots of each polynomial equation.
3
2
49. x + 2x + 3x + 6 = 0
50. x  3x + 4x  12 = 0
3
2