Name ______Date ______Pd ______
Advanced Algebra – Unit 2 – Review
A.APR.1/A.SSE.1 Polynomial Operations
State the degree and leading coefficient of each polynomial:
Degree Leading Coefficient Number of Terms Polynomial
1.______
2.______
3.______
Perform each operation indicated and simplify the final expression.
4.
5.
6.
A.SSE.2 Factoring
Factor each completely
7.
8.
9.
10. Give the GCF(Greatest Common Factor) for
A-APR.2 Remainder Theorem / Factor Theorem
11. Find the remainder for divided by Is x – 1 a factor of ?
13. Divide by .
14. If f(2) = 0 for some function f(x), which of the following must be true?
a) (x + 2) is a factor of f(x)
b) ( x – 2) is a facotr of f(x)
c) -2 is a zero of f(x)
d) none of these
A-APR.3 Identifying Zeros
16. Identify the zeros for the function
17. Identify the zeros for the function
18. Identify the zeros for the function of the graph shown to the right:
19. What is the possible number of real zeros for ?
20. What is the possible number of imaginary zeros for ?
F-IF.7 – End Behavior / Descartes Rule of Signs / Multiplicity / Rational Root Theorem
Use the graph to the right to answer the
questions below. Pay close attention to
the fact that the x-axis has increments
of 1 and the y-axis has increments of 5.
______22. The sign of the leading coefficient for the function is (Positive or Negative)
______23. The degree of the function is (Even or Odd)
______24. Which root(s) have a multiplicity that is even?
______25. What is the minimum degree for the function?
26. The extremum that is located near the point (2,0) is considered to be a(n):
A) Relative MaximumB) Absolute Maximum
C) Relative MinimumD) Absolute Minimum
27. Using multiplicity, write the factored form of the function that creates the graph.
28. List ALL the possible rational roots of
29. How many positive real roots does have?
30. How many negative real roots does have?
31. Sketch the graph of a polynomial function that would have a leading term
32. Which of the following describes the end behavior of the function ?
33. Make a reasonable sketch of the graph of the most general polynomial function which satisfies the given conditions:
The leading coefficient is NEGATIVE and the degree is 3. The zeros of the function are:
-2 (multiplicity of 2), -1 (multiplicity of 1), 3(multiplicity of 2)
34. Write the polynomial function in factor form for the graph on #33.
______
Name ______Date ______Pd ______
Advanced Algebra - A-REI.7 – A.REI.11 Systems of Equations (Linear and Polynomial)
Find the point(s) of intersection (POI) for each system.
1. 2.
POI ______POI ______
3.
POI ______
-4 / 32-3 / 20
-2 / 15
-1 / 8
0 / 0
1 / 6
2 / 12
3 / 15
4 / 19
-4 / 35
-3 / 30
-2 / 24
-1 / 32
0 / 22
1 / 12
2 / 12
3 / 17
4 / 21
4. The points of intersection for f(x) and g(x) in
the tables below are:
POI ______