Algebra 2
Review Chapter 6
Name ____________________
1. Write each polynomial in standard form. Then classify it by degree and by number of terms.
a. 3x  7 x  9  x
2
4
b. 2 x ( x  3)( x  2)
4
2. 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.
3.
x3  4 x2  5  0
4. x  3  4  x  x
2
3
5. Write a polynomial function with rational coefficients in standard form with the given zeros.
a. 1,1,2
b. -3,0,0,1
c. -2,-2,-2
6. For each function, find the zeros and state the multiplicity of multiple zeros.
a.
y  ( x  4)( x  5)3
b.
3s 2 ( s  4)3 ( s  2)2 ( s  1)
7. Solve each equation. Find the zeros by factoring.
a. (x – 3)(x2 + 3x – 4)
b. x  2 x  x  0
3
2
8. Divide using long division.
( x 3  7 x 2  5x  6)  ( x  2)
9. Divide using synthetic division.
a.
( x 4  x  2)  ( x  1)
b. ( x
3
 3x 2  2 x  4)  ( x  2)
10. Use the Rational Root Theorem to list all possible rational roots for each equation. Then find all roots.
a. x  6 x  11x  6  0
3
2
b. x  6 x  13x  12 x  4  0
4
3
2
11. Use synthetic division and the remainder Theorem to find P(a).
P( x)  5x 4  x 2  1; a  2
20. Factor the expression using the difference of cubes.
x 3 - 1000
21. Factor the expression using the sum of cubes. Then solve to find all the complex roots.
x3 + 64 = 0
Answer Key
1a. 8 x  3x  9 ; quartic trinomial
4
b.
y = .0096x3 - .38x2 + 3.54x + 58.96
2a.
3.
2
b. about 59 employees
-1, 1.38, 3.62
4.
5.a.
f ( x)  x 3  4 x 2  5x  2
c.
f ( x)  x 3  6 x 2  12 x  8
6a.
-4, 5 (multiplicity 3)
3
8 x 2  x ; quadratic binomial
8
-1.78
b.
b.
7a. 3, -4, 1
f ( x )  x 4  2 x 3  3x 2
0 (mult. 2), 2 (mult. 3), -2 (mult. 2), 1
b.
0,1
8. x  5 x  15 R24
2
9a.
x 3  x 2  x  2 R4
b. x  5 x  8 R12
2
1, 2, 3, 6 ; roots: 1, 2, 3
b. possible rational roots: 1, 2, 4 ; roots: -1, -2
10a. possible rational roots:
11. 77
12. (x – 10) (x2 + 10x + 100)
13.
-4, 2
 2i 3 or -4, 2  3.46i
Answer Key
1a. 8 x  3x  9 ; quartic trinomial
4
b.
y = .0096x3 - .38x2 + 3.54x + 58.96
2a.
3.
2
b. about 59 employees
-1, 1.38, 3.62
4.
5.a.
f ( x)  x 3  4 x 2  5x  2
c.
f ( x)  x 3  6 x 2  12 x  8
6a.
-4, 5 (multiplicity 3)
3
8 x 2  x ; quadratic binomial
8
-1.78
b.
b.
7a. 3, -4, 1
f ( x )  x 4  2 x 3  3x 2
0 (mult. 2), 2 (mult. 3), -2 (mult. 2), 1
b.
0,1
8. x  5 x  15 R24
2
9a.
x 3  x 2  x  2 R4
b. x  5 x  8 R12
2
1, 2, 3, 6 ; roots: 1, 2, 3
1, 2, 4 ; roots: -1, -2
10a. possible rational roots:
b.
possible rational roots:
11. 77
12. (x – 10) (x2 + 10x + 100)
13.
-4, 2
 2i 3 or -4, 2  3.46i