Algebra 2
Chapter 3 Review
Name______________________________
Period__________
Fill in the blank.
1. The number of times (x – r) is a factor of P(x) is the ____________________ of r.
2.
The ____________________ of a function is a description of the function values as x
approaches positive infinity or negative infinity.
Rewrite each polynomial in standard form. Then identify the leading coefficient, degree,
and number of terms. Name the polynomial.
3.
4 x 2  3x3  6 x  7
4. 1  11x  9 x 2
Add or subtract. Write your answer in standard form.
5.
(8x3  4 x 2  3x  1)  (1  5 x 2  x)
6. ( x 4  x 2  4)  ( x 2  x3  5x 4  7)
Graph each polynomial function on a calculator. Describe the graph, and identify the
number of real zeros.
7. f ( x)   x 4  4 x 2  1
8. f ( x)  x3  3x 2  2
Find each product.
9. 3x(2 x 2  6 x  1)
10. ab2 (a 2  a  ab)
11. (2 x  5)( x3  x 2  1)
12. ( x  3)3
13. (2 x  1)4
14. A cylinder has a height of x 2  x  3 and a radius of 2x. Write an equation for the volume.
Simplify so it is a sum of monomials.
Divide using long division.
15. ( x3  5 x 2  2 x  7)  ( x  2)
16. (8 x 4  6 x 2  2 x  4)  (2 x  1)
Divide using synthetic division.
17. ( x3  4 x 2  3x  2)  ( x  3)
18. ( x3  2 x  1)  ( x  2)
Determine whether the given binomial is a factor of the polynomial P(x).
19. ( x  3); P( x)  x3  2 x 2  5
20. ( x  1); P( x)  4 x 4  5 x 2  3x  2
Factor each expression. (Do not solve).
21. x3  x 2  16 x  16
22. 4 x 3  8 x 2  x  2
23. 3 x 3  81
24. 16 x 3  2
25. x 4  x 2  12
Identify all the real roots of each equation. Do these by hand.
26. x3  5 x 2  8 x  4  0
27. x3  6 x 2  9 x  2  0
28. x 4  12 x 2  27  0
29. x3  5 x 2  4  0
Write the simplest polynomial function with the given roots.
30.  2,  1
31. 3,i
Solve by finding all roots. Do by hand.
32. x3  x 2  4 x  4  0
33. x 4  x 2  2  0
Identify the leading coefficient, degree, and end behavior.
34. 2 x 3  5 x 2  3
35. x 4  2 x3  3x  1
36. 7 x5  x 4  2 x 2  6
37. Draw a graph of an even function with exactly three real zeros and a positive leading
coefficient.
Graph by hand.
38. f ( x)  x3  x 2  5 x  6
39. g ( x)  x 4  10 x 2  9