Quiz Review 5.1-5.6 & 5.8
Name: ____________
1. What is the polynomial represented by the factors (x – 9), (x -4), and (x + 8)? (Use standard form)
2. What is the complete factorization of c3 -3c2 -4c + 12?
3. What is the polynomial function whose zeros are –6, 0, and 18? (Use standard form)
4. What are the solutions of x5  3x 4  5 x3  15 x 2  4 x  12
5. What is the quotient of
(3x3– 14x2 + 16x-22) and (x – 4)?
6. How many roots does the function f(x) = 4x7 + x2 have?
7. What is the left end behavior of: g ( x)   x5  3x 4  12 ?
8. How would you classify given polynomial? f(x) = -6x2+ 2x4 -
71
9. What is the lowest degree of the function in the graph?
10. Write the factors appear to be part of the polynomial in the graph below?
Divide
11. f(x) = x3  3 x 2  x  10 by x 2  3x  1
12. f(x) =
2 x3  7 x 2  8 x  28 by 2x -7
13. Using the remainder theorem find the j(-2)
j(x) = 5 x 4  2 x 2 15 x  10
13)__________________________________
Please use words and/or sentences to answer the following questions.
14. Why is (x + 2)2 NOT equivalent to x2+ 4?
15. The zeros of a function are -7, 2, and 0. What
are the factors that match those zeros?
16. Explain what is meant by
the end behavior of a
polynomial.
17. What division does this problem represent?
1 5 2 24
2
2 14 24 .
1 7 12
0
What conclusions can you give from this problem?
18. Graph f(x) = 3x 2 ( x  2)2
x
y
Increasing Intervals:__________________
Decreasing Intervals:_________________
19. Find all of the zeros of the polynomial. (no
decimals!)
g(x) = x 4  4 x3  7 x 2  16 x  12
20. Given the polynomial
f ( x)  2 x 3  7 x 2  9
a. List all possible rational zeros.
b. Factor polynomial completely
Find the Roots/Zeros
Answer
Answer
x=−2,
2
3
c. List all zeros of the function.
21. Simplify completely
x3 y 4 2( x 3 )2
x 5 x3 y 2
22. What is equivalent to (3x3  x 2  3)  (2 x3  6 x 2  3x  1)
23. Simplify (3x  2) 2
24. Simplify
 3x 2 y 0 z 


3
 y

3
25. Classify the following functions. Decide if the function is a polynomial function.
If it is a polynomial function, state its degree, type, leading coefficient and general shape.
a. f(x) = 2 x – ⅔x
b. f ( x)  x 4 3  x  5
c. f ( x)  x  5x3  3
Polynomial?______
Degree:______ L.C.:_______
Type:______________
Polynomial?______
Degree:______
L.C.:_______
Type:______________
Polynomial?______
Degree:______
L.C.:_______
Type:______________
26.
Draw simplified graphs of following functions
Consider x-intercepts, end behavior, and double roots
f(x)= - (x+1)2(x-2)(x+3)
h(x)= x (x+3) 2
27. Find all the following information for polynomial graphed below:
Number of turning points:____
Lowest Degree:______
Is the leading coefficient positive or negative? __________
Real Zeros:________________
y-intercept:______
Relative maximum(s):_______________________
Relative Minimum(s):_______________________
As x +, f(x) ____
As x -, f(x) ____
Increasing Intervals: _______________________________
Decreasing Intervals: _______________________________