1.
Write a polynomial equation of least degree with roots -1, 2
i
, and -2
i
.
A.
x
3
+
x
2
- 4
x
+ 4 = 0
B.
x
3
-
x
2
+ 4
x
+ 4 = 0
C.
3
x
+
x
2
+ 4
x
- 4 = 0
D.
x
3
+
x
2
+ 4
x
+ 4 = 0
Hint
2.
In the equation
x
3
+
x
2
+ 4
x
+ 4 = 0, how many times does the graph of the related function cross the
x
-axis?
A.
2
B.
3
C.
1
D.
0
Hint
3.
If you solve
x
2
- 8
x
- 20 = 0 by the method of completing the square, add 20 to each side and then ____.
A.
add 4 to each side
B.
add 16 to each side
C.
add 8 to each side
D.
add 32 to each side
Hint
4.
Solve the equation 2
x
2
-
x
+ 4 = 0 by any method.
A.
i
B.
i
C.
1
i
D.
i
Hint
5.
Divide
x
4
+ 2
x
2
- 1 by
x
- 1 using synthetic division. The result of synthetic division is ____.
A.
1 3 1 3 | -2
B.
1 1 3 3 | 2
C.
1 3 1 3 | 2
D.
1 1 3 3 | -2
Hint
6.
Find the value of
k
so that the remainder of (
x
3
- 3
x
2
+
kx
- 6) ÷ (
x
+ 2) is 0.
A.
k
= 11
B.
k
= 6
C.
k
= -11
D.
k
= -13
Hint
7.
List the possible rational roots of 3
x
3
+ 5
x
2
- 2
x
+ 1 = 0.
A.
,
B.
,
C.
1,
D.
1,
Hint
8.
Find the number of positive real zeros for
f
(
x
) = 3
x
5
+ 2
x
3
+
x
2
+ 7
x
- 1 = 0.
A.
exactly 1 positive real zero
B.
4 or 2 or 0 positive real zeros
C.
no positive real zeros
D.
4 or 2 positive real zeros
Hint
9.
Approximate the real zeros of the function
f
(
x
) = 2
x
2
+ 4
x
+ 1 to the nearest tenth.
A.
-1.7 and -0.3
B.
-1.8 and -0.4
C.
-1.6 and -0.2
D.
-1.8 and -0.2
Hint
10.
Determine the number of complex zeros of the function
f
(
x
) =
x
5
- 4
x
2
+ 2
x
- 1.
A.
5
B.
3
C.
4
D.
2
Hint
11.
Solve
= 3.
A.
-1
B.
3
C.
2
D.
2, 3
Hint
12.
Decompose
into partial fractions.
A.
B.
C.
D.
Hint
13.
Solve
.
A.
-10
B.
4
C.
-6
D.
8
Hint
14.
Solve
4.
A.
x
0
B.
x
8
C.
none of these
D.
0
x
8
Hint
15.
How many direction changes are there in the graph of a linear equation?
A.
0
B.
2
C.
3
D.
1
Hint
16.
Use a graphing calculator to write a polynomial function to model the set of data.
A.
1.3
x
+ 0.9
B.
1.3
x
- 0.9
C.
0.9
x
+ 1.3
D.
0.9
x
- 1.3
Hint