Rich – AAT (H)
Name: _________________________________
Review Unit 2 Part B Higher Ordered Polynomials Test
Date: ____________________ Period: _______
LT 2.B.1: use the leading coefficient test to determine end behavior of graphs of polynomials. LT 2.B.2: determine if polynomial
functions are even or odd degree. LT 2.B.3: sketch the graph of a function using the leading coefficients, zeros, and other needed
solution points.
#1 – 6: Match each function with its graph. Write the letter corresponding to the correct answer on the
line provided (non calc).
1. f (x)   x 3  x 2  2x
_______
2. f (x)  x 3  2x 2  x  2
_______
3. f (x)   x 4  4 x 3  3x 2
_______
4. f (x)   x 2  3
_______
1
5. f (x)  x 2  x  1
4
_______
6. f (x)  x 4  2x 3  7x 2  8 x  12
_______
A.
B.
C.
D.
E.
F.
#7: Sketch a graph of the polynomial with the given characteristics (non-calc).
7. An even degree polynomial with a positive
leading coefficient and zeros of x = -4, 0, and 3 (multiplicity of 2)
#8 – 9: Use the graph to fill in the blanks below (non-calc).
8.
9.
 1.55, 0.63
 0, 5 
 0.22, 2.11
1.41, 9 
 1.41, 9
Least Degree (#): ____ Even or Odd Degree: ______
Least Degree (#): ___ Even or Odd Degree: ______
Zeros (how many and what type?):______________
Zeros (how many and what type?): ____________
__________________________________________
______________________________________
Between which two consecutive #s are the real zeros?
What are the real zeros? __________________
___________________________________________
Leading Coefficient (Describe it): _______________
Leading Coefficient (Describe it): ____________
End Behavior: lim f ( x)  _____ lim f ( x)  _____
End Behavior: lim f ( x)  _____ lim f ( x)  ____
x 
x 
x 
x 
Increasing: ______________________________
Increasing: _____________________________
Decreasing: ______________________________
Decreasing: ______________________________
LT 2.B.7: use long division to divide polynomials. LT 2.B.8: use synthetic division to divide polynomials by binomials in the form
(x – k).
#10 – 13: Divide each polynomial. Be careful when choosing long or synthetic division (non-calc).
10.
5x 3  13x 2  x  2
x 2  3x  1


11. 2x 3  19 x2  38 x  24  x  4 
1
12.
3x 4
x2  1
13.  3x 3  20 x 2  29 x  12    x  3 
LT 2.B.9: use the Factor Theorem. LT 2.B.4: find zeros of polynomial functions.
#14 – 17: Verify that each of the given binomials is a factor of the polynomial. Then find the remaining
factors and identify all zeros of the polynomial function (non-calc).
14. f  x   20x 4  9x 3  14 x2  3x;
 4 x  3
16. f  x   x 4  11x 3  41x2  61x  30;  x  2 x  5
15. f  x   3x 3  8x2  20x  16;
 x  4
17. f  x   3x 3  12x2  12x;
 x  2
LT 2.B.5: use the zeros of a polynomial to write an appropriate equation. LT 2.B.11: find conjugate pairs of complex zeros.
#18 – 19: Find a polynomial function with real coefficients that has the given zeros (non-calc).
2
18. x  , 4, 3i  be careful !
3
19. x  0  multiplicity of 3  ,  4,
1
2
LT 2.B.10: find all of the zeros of a polynomial by using the graphing utility to find one real zero and polynomial division to find
the rest.
#20 – 26: Find all of the zeros of the polynomial functions, using a calculator as an aide. You must show
all work after finding the first one (3rd degree) or two (4th degree) zeros (calc).
20. f  x   2x 3  11x2  21x  90
21. f  x   x 4  4 x 3  7x2  22x  24
22. f  x   x 3  6x
23. f  x   x 4  2x 3  20x 2  8x  96
24. f  x   x 3  x2  4 x  4
25. f  x   x 4  x 3  23x 2  x  70
26. f  x   2x 4  9x 3  11x2  30x
LT 2.B.6: use polynomial equations to model real life problems.
#27 – 28: Use the given information to find the missing measures of the object (non-calc).
24. The volume of a rectangular prism is given by V  x   6x 3  23x2  6x  8 . Find the missing measures.
?
2x – 1
?
25. The area of a triangle is given by A x   9x2  3x  20 if the base of the triangle measures  6 x  10 
centimeters. Find the height of the triangle.