COLLEGE ALGEBRA
MATH 110
Southwestern   
Adventist University 
 
   Distance Education Lawrence E. Turner, Jr., Ph.D.  


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SAMPLE TEST QUESTIONS

1999

(Barnett, Ziegler, and Byleen)


Chapter 4     Polynomials and Rational Functions

4.1     polynomial functions and graphs

50.     For each of the following divide f(x) by g(x) and calculate the quotient q(x) and the remainder r(x).
  1.  
    (10)
  2.  
    (10)
  3.  
    (10)
  4.  
    (10)

51.     When you divide a polynomial of degree n, P(x), by a linear factor (x-a),
  1. what is the degree of the quotient?
    (2)
  2. what possible remainders might you obtain?
    (2)
  3. show that the remainder is equal to P(a).
    (5)
  4. if (x-a) happens to be a factor, then what is the remainder?
    (2)

52.     Evaluate the following polynomial functions at the indicated valus of x:
  1.  
    (5)
  2.  
    (5)

53.     Use synthetic division to determine the quotient and remainder for:
  1.  
    (5)
  2.  
    (5)

54.     A polynomial crosses the x-axis at x = -2, 1, and 4. What are its real factors?
(5)


55.     A polynomial crosses the x-axis at x = 3 and just touches it at x = -2. What are its real factors?
(5)


56.     What are the zeros of the following function?
(5)


57.     A polynomial function crosses the x-axis in four places. When x is large, both positive and negative, the value of the function is positive and large. What is the degree of the polynomial? Explain.
(5)


4.2     finding rational zeros of polynomials

58.     Find all the zeros for the following functions:
  1.  
    (15)
  2.  
    (15)
  3.  
    (15)
  4.  
    (15)

    Hints: are there any common factors?
      how many potential positive real zeros?
      how many potential negative real zeros?
      what are the potential rational zeros?
      can you factor by inspection or use a formula to find any remaining zeros?

59.     One zero of the following polynomial is 2i. Find one other zero.
(5)


60.     One zero of the following polynomial is 2i. Find all the zeros.

(10)


61.     The following function can be factored as

find its zeros.

(5)


4.3     approximating real zeros of polynomials

62.     What are the possible rational zeros of each of the following functions?
  1.  
    (5)
  2.  
    (5)
  3.  
    (5)

63.     Determine the number of possible positive real zeros, the number of possible negative real zeroes, the number of possible complex zeros of:
  1.  
    (5)
  2.  
    (5)

    That is, make a table of possible configurations of the zeros:

    pos real zerosneg real zeros complex zerostotal zeros
    		     

64.     Evaluating the following equation at integer points yields:


    xf(x)
    125
    2-42
    3-45
    488
    5429
    xf(x)
    -163
    -2-110
    -3-507
    -4-1200
       
  1. What are the intervals within which real zeros may be found?
    (5)
  2. Are there any complex zeros? Why or why not?
    (5)

65.     Find the integer values for the upper and lower bounds of the real zeros for:
(5)


4.4    rational functions

66.     For each of the following functions, determine any vertical and horizontal asymptotes:
  1.  
    (10)
  2.  
    (10)
  3.  
    (10)
  4.  
    (10)
  5.  
    (10)
  6.  
    (10)

67.     For each of the following functions, determine any vertical and horizontal asymptotes and sketch the graph of the function:
  1.  
    (15)
  2.  
    (15)
  3.  
    (15)

68.     Write out a rational function that has vertical asymptotes at x = -2 and x = 3 and has an oblique asympotote. Hint, there are many possible answers--just write out one example.
(5)
  
© 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008 by Lawrence Turner