Name______________________________
Date__________ Period__________
Algebra 2 – Chapter 6 Test
Write each polynomial in standard form. Then classify it by degree and number of terms.
1. 9 x  2 x  3 x
2
2
2. 4 x( x  5)( x  6)
Standard Form _____________
Standard Form __________
Degree ________________
Degree ________________
Terms _________________
Terms _________________
3. The table shows data on the number of employees that a small company had from 1975 to 2000.
Let 0 represent 1975.
Year
# of
Employees
1975 =
year 0
60
1980
1985
1990
1995
2000
65
70
60
55
64
a.
Find a cubic model for the set of values.
b.
Use your model to estimate the number of employees in 1998.
Solve each equation by graphing. Where necessary, round to the nearest hundredth.
4.
y  x 3  3x 2  x  3
zeros: _______________
5.  x  3 x  4  0
3
zeros: ________________
6. x  6 x  1  0
2
zeros: ________________
Write a polynomial function with rational coefficients in Standard Form with the given zeros.
7. 2, 3, 5
8. -1, -1, 1
For each function, determine the zeros and their multiplicity.
9.
y  ( x  1) 2 (2 x  3) 3
10.
y  4 x 2 ( x  2) 3 ( x  1)
Name______________________________
Date__________ Period__________
Solve each equation by factoring.
11.
12. x  10 x  16 x  0
( x  1)( x 2  5 x  6)  0
3
2
Divide using long division.
13.
(2 x 3  13x 2  17 x  10)  ( x  5)
14.
( x 3  9 x 2  26 x  24)  ( x  4)
16.
(2 x 3  4 x  3)  ( x  1)
Divide using synthetic division.
15.
( x 3  4 x 2  x  5)  ( x  2)
Use the Rational Root Theorem to list all possible rational roots for each equation. Which possible solutions work.?
18. x  2 x  3 x  6  0
3
2
19. x  3x  x  3  0
3
2
20. Factor the expression x3 + 64.
21. Solve the expression x3 – 125 = 0 to find all of the complex roots.