Advanced Math
Quiz 3.1-3.3 Review
Name:
Dec. 2013
Use Synthetic Division to divide the first polynomial by the second polynomial.
1.
1.
Quotient:__________________
Remainder:________________
2.
2.
Quotient:__________________
Remainder:________________
3.
3.
Quotient:__________________
Remainder:________________
4.
4.
Quotient:__________________
Remainder:________________
5.
5.
Quotient:__________________
Remainder:________________
6.
6.
Quotient:__________________
Remainder:________________
Use Synthetic Division and the Remainder Theorem to find ( ).
7.
( )
7.
Remainder with Synthetic Division:_________________
Remainder with the Remainder Theorem:____________
8.
( )
8.
Remainder with Synthetic Division:_________________
Remainder with the Remainder Theorem:____________
9.
( )
9.
Remainder with Synthetic Division:_________________
Remainder with the Remainder Theorem:____________
10.
( )
10.
Remainder with Synthetic Division:_________________
Remainder with the Remainder Theorem:____________
Use Synthetic Division and the Factor Theorem to determine whether the given binomial is a factor of ( ).
11.
( )
11._______________________
12.
( )
12._______________________
13.
( )
13._______________________
14.
( )
14._______________________
Examine the leading term and the degree of the polynomial to determine the far-left and far-right behavior of the
graph.
15.
( )
Degree___________
Sign of Leading Coefficient_________________
End Behavior:_______________________________________________
_____________________________________________
As
16.
( )
( )
Degree___________
As
( )
Sign of Leading Coefficient_________________
End Behavior:_______________________________________________
_____________________________________________
As
17.
( )
( )
Degree___________
As
( )
Sign of Leading Coefficient_________________
End Behavior:_______________________________________________
_____________________________________________
As
18.
( )
( )
Degree___________
As
( )
Sign of Leading Coefficient_________________
End Behavior:_______________________________________________
_____________________________________________
As
19.
( )
( )
Degree___________
As
( )
Sign of Leading Coefficient_________________
End Behavior:_______________________________________________
_____________________________________________
As
20.
( )
( )
Degree___________
As
( )
Sign of Leading Coefficient_________________
End Behavior:_______________________________________________
_____________________________________________
As
( )
As
( )
Given the graphs, determine the “far-right” and “far-left” behavior.
( )
21.
22.
( )
( )
( )
23.
( )
( )
Find the real zeros of each polynomial function by factoring. The number in parentheses to the right of each
polynomial indicates the number of real zeros of the given polynomial function.
24.
( )
25.
( )
26.
( )
27.
( )
( )
( )
24._______________________
25._______________________
( )
( )
26._______________________
27._______________________
Use the Intermediate Value Theorem to verify that ( ) has a zero between
between a and b.
28.
( )
28.
. Explain why there is a zero
_______________________________________
_______________________________________
29.
( )
29.
_______________________________________
_______________________________________
30.
( )
30.
_______________________________________
_______________________________________
31.
( )
31.
_______________________________________
_______________________________________
Procedure for graphing:
1. Start by graphing the zeros
2. Then determine whether the graph passes through the zero or hits and bounces off the zero
3. Graph (if possible) the y-intercept
4. Determine the end behavior – which way should the arrows go?
5. Create a smooth curve
32.
( )
(
)(
)(
)
What is the degree of the polynomial?_________
What kind of number is the degree?___________
What is the sign of the leading coefficient?_____
What is the end behavior?
( )
As
( )
As
What are the x-intercepts (zeros) & their multiplicities?
_____________ multiplicity_______ pass through/bounce
_____________ multiplicity_______ pass through/bounce
What is the y-intercept? [plug in x = 0] _______________
You will only graph this if it fits – if it doesn’t, just estimate!
33.
( )
(
) (
)
What is the degree of the polynomial?_________
What kind of number is the degree?___________
What is the sign of the leading coefficient?_____
What is the end behavior?
( )
As
( )
As
What are the x-intercepts (zeros) & their multiplicities?
_____________ multiplicity_______ pass through/bounce
_____________ multiplicity_______ pass through/bounce
What is the y-intercept? [plug in x = 0] _______________
You will only graph this if it fits – if it doesn’t, just estimate!
34.
( )
(
) (
)
What is the degree of the polynomial?_________
What kind of number is the degree?___________
What is the sign of the leading coefficient?_____
What is the end behavior?
( )
As
( )
As
What are the x-intercepts (zeros) & their multiplicities?
_____________ multiplicity_______ pass through/bounce
_____________ multiplicity_______ pass through/bounce
What is the y-intercept? [plug in x = 0] _______________
You will only graph this if it fits – if it doesn’t, just estimate!
35.
( )
(
)
What is the degree of the polynomial?_________
What kind of number is the degree?___________
What is the sign of the leading coefficient?_____
What is the end behavior?
( )
As
( )
As
What are the x-intercepts (zeros) & their multiplicities?
_____________ multiplicity_______ pass through/bounce
_____________ multiplicity_______ pass through/bounce
What is the y-intercept? [plug in x = 0] _______________
You will only graph this if it fits – if it doesn’t, just estimate!
36.
( )
(
) (
)
What is the degree of the polynomial?_________
What kind of number is the degree?___________
What is the sign of the leading coefficient?_____
What is the end behavior?
( )
As
( )
As
What are the x-intercepts (zeros) & their multiplicities?
_____________ multiplicity_______ pass through/bounce
_____________ multiplicity_______ pass through/bounce
What is the y-intercept? [plug in x = 0] _______________
You will only graph this if it fits – if it doesn’t, just estimate!
37.
( )
(
)(
) (
)
What is the degree of the polynomial?_________
What kind of number is the degree?___________
What is the sign of the leading coefficient?_____
What is the end behavior?
( )
As
( )
As
What are the x-intercepts (zeros) & their multiplicities?
_____________ multiplicity_______ pass through/bounce
_____________ multiplicity_______ pass through/bounce
What is the y-intercept? [plug in x = 0] _______________
You will only graph this if it fits – if it doesn’t, just estimate!
38.
( )
(
)
What is the degree of the polynomial?_________
What kind of number is the degree?___________
What is the sign of the leading coefficient?_____
What is the end behavior?
( )
As
( )
As
What are the x-intercepts (zeros) & their multiplicities?
_____________ multiplicity_______ pass through/bounce
_____________ multiplicity_______ pass through/bounce
What is the y-intercept? [plug in x = 0] _______________
You will only graph this if it fits – if it doesn’t, just estimate!
Find the real zeros of ( ) using the Rational Root Theorem.
39.
Given ( )
Degree = __________
Factors of
List of possible rational zeros:
Start the synthetic division with
40.
Given ( )
What are the rational zeros of ( )?___________________
Degree = __________
Factors of
List of possible rational zeros:
Start the synthetic division with
Number of Zeros = _________
________
Factors of
Number of Zeros = _________
________
Factors of
What are the rational zeros of ( )?___________________
41.
Given ( )
Degree = __________
Factors of
List of possible rational zeros:
Start the synthetic division with
42.
Given ( )
What are the rational zeros of ( )?___________________
Degree = __________
Factors of
List of possible rational zeros:
Start the synthetic division with
Number of Zeros = _________
________
Factors of
Number of Zeros = _________
________
Factors of
What are the rational zeros of ( )?___________________