Math 3 Hon: Unit 4 Quiz Review
Name: _________________________
4
3
2
I. Use the function f ( x )  3 x  2 x  9 x  2 x  8
a. What is the leading coefficient?
1. ________________________________
b. What is the degree of the polynomial?
2. ________________________________
c. Find f (2)
3. ________________________________
d. Find the zeroes of this function:
4. ________________________________
e. Find all maximums and minimums:
5. ________________________________
(label each as relative or absolute)
f. Describe the end behavior:
________________________________
6. ________________________________
________________________________
II. Graph Interpretation
GRAPH #1:
GRAPH #2:
a. State the number of REAL zeroes: ________
a. State the number of REAL zeroes: ________
b. State the number of COMPLEX zeroes: ____
b. State the number of COMPLEX zeroes: ____
c. What is the possible degree? _____________
c. What is the possible degree? _____________
d. Is the leading coefficient positive or
negative?
d. Is the leading coefficient positive or
negative?
e. What is the End Behavior?
e. What is the End Behavior?
GRAPH #4:
GRAPH #3:
(-5, 3)
(-3, 13)
(3, -1)
0)(-7, 0)
(6, 0)
(-2, 0)
(-4,
(0, 0)
(4, -6)
(0, -4)
(1, -10)
(5, -6)
a. Degree? ___________
a. Degree? ___________
b. Leading Coefficient? _________
b. Leading Coefficient? _________
c. Zeroes/Roots:
c. Zeroes/Roots:
REAL? ______ COMPLEX? ______
REAL? ______ COMPLEX? ______
d. Identify all Maximums:
d. Identify all Maximums:
e. Identify All Minimums:
e. Identify All Minimums:
Use Interval or Inequality Notation:
Use Interval or Inequality Notation:
f. Where is the graph POSITIVE?
f. Where is the graph POSITIVE?
g. Where is the graph NEGATIVE?
g. Where is the graph NEGATIVE?
h. Where is the graph INCREASING?
h. Where is the graph INCREASING?
i. Where is the graph DECREASING?
i. Where is the graph DECREASING?
j. What is the RANGE of this graph?
j. What is the RANGE of this graph?
III. U-SUBSTITUTION: Find exact values of all zeroes.
1.
x4  3 x2  2  0
5.
x6  7 x3  6  0
2.
6 x4  7 x2  3  0
6.
x6  2 x4  x2  0
3.
x  4 x  45  0
7.
2 x5  7 x3  4 x  0
4.
x 2 / 3  5 x 1 / 3  14  0
8.
x  x  42  0
IV. Find if each binomial is a factor of the given polynomial.
9.
Polynomial=
x 3  x 2  10 x  8
10. Polynomial= 2 x  5 x  28 x  15
2
Factor = x – 5?
V. RATIONAL ROOT THEOREM:
List all possible real zeros first.
Final all exact zeros for each function.
13.
x 3  6 x 2  11 x  6
Factor = x – 2?
Factor = x + 1
3
11. Polynomial=
x 3  6 x 2  10 x  8
12. Polynomial=
2 x 3  7 x 2  53 x  28
Factor = 2x + 1?
14.
x 3  3 x 2  25 x  21
15.
x 4  10 x 3  33 x 2  38 x  8
16.
x3  3x  2
17.
6 x 3  11 x 2  3 x  2
VI. Write the Polynomial Function for the given roots. All terms with integer
coefficients
18. Roots = 3, -2, 5
21. Roots = 3 + 2i, 7
19. Roots = -4i, 4i
22. Roots = 1 ± i, - 4
20. Roots = 2, 5i
23. Roots = 2 ± i, 3 ± 2i