Algebra II- Review Chapter 6
Algebra 2 Name ______________________________
Review Unit 4 Polynomials
1. Write each polynomial in standard form. Then classify it by degree and by number of terms.
a. [pic] b. [pic]
Standard Form: ________________________ Standard Form: ___________________________
Classification:______________ _________________ Classification:_____________ ______________
2. Describe the end behaviors of the functions below. Then, build a table and graph.
a) [pic] b) [pic]
End behavior: _____ _____ End behavior: _____ _____
3. Add, subtract, or multiply.
a) [pic]
b)[pic]
c) [pic]
d)[pic]
4. For each function, find the zeros and state the multiplicity of multiple zeros.
a. [pic] b. y = [pic]
5. Write each polynomial in FACTORED FORM and SOLVE each equation. (Hint – find the Zeros by factoring.)
a. [pic] b. [pic]
Factored Form:_________________ Factored Form:_________________
Zeros:________________________ Zeros:_________________________
6. Divide using long division.
a. [pic] b. [pic]
7. Divide using synthetic division.
a.[pic] b.[pic]
8. Given the following polynomial functions and one of its zeros, find all the zeros/solutions of the polynomial.
***INCLUDE THE GIVEN ZERO IN YOUR ANSWER!
a.[pic]; given: [pic]is a zero b. [pic] ; given: [pic]is a zero
Zeros: ________________________________ Zeros:_____________________________________
9. Graph.
a. y = (x + 4)(x - 3)(x + 2) b. y = -x(x – 5)2(x + 3)
Zeros: _______________________ Zeros: _______________________
End Behavior: ______________ End Behavior: __________________
10. Given each graph, write a function in factored form
a) b)
Function:____________________ Function:____________________
11. Use the remainder theorem to find P(4) for [pic]
12. Given [pic], complete the following:
Find the zeros by factoring:____________
Find the y-intercept:_________________
Describe the end behavior:____________
Sketch a graph:
13. Use the rational root theorem to list all possible rational solutions to [pic]
14. Use the rational root theorem to explain why x = 5 is not a possible rational root of [pic].
15. Write a polynomial function with rational coefficients in FACTORED FORM with the given zeros.
Then convert Factored Form into Standard Form. x = 6, 1, 2
16. Factor the expression using the sum or difference of cubes. (And Find the Solutions).
a. x3 – 1000 b. 27x3 + 64
17. FACTOR completely and SOLVE. [pic]
Use the Rational Root Theorem to list all possible rational roots for each equation.
Then find any actual roots.
18. x3 + 6x2 + x + 6 = 0
-----------------------
|x |y |
|-3 | |
|-2 | |
|-1 | |
|0 | |
|1 | |
|2 | |
[pic]
[pic]
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