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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