Answers to the Sample Test!!
 
1)  Use the remainder from each synthetic substitution to find the value( remainder theorem).
           Answers are:
                                     a)  -39
                                     b)  86
                                     c)  19/4 or 4 and  3/4
                                     d) 15/4 or  3 and  3/4


2)  Since the leading coefficient is 2 and the linear term is -5 and p(0) = 7  this means the polynomial is in the form:       2x3 + bx2 - 5x + 7.  Use the fact that p(2) = 21 to get the function.
21 = 16 + 4b - 10 + 7
21 = 4b + 13
8 = 4b
b = 2
The function is p(x) = 2x3 + 2x2 - 5x + 7
Now use synthetic division to find p(-1)
Answer is 12


3)  a)  -4
     b)  9
     c)  0
     d)  -7


4)  Dividing by 1 gives you        1  -9  26  -24  0
     Dividing by 3 gives you        1  -6  8  0  This represents the function
                                                x2 - 6x + 8  which factors to:
                                                (x - 2)(x - 4)
The other zeros are 2 and 4


5)                                                                               a)
 
 
b)

 
c)

d)



6) 

             A(x) = x(900- 3x)/ 2 = 450x - (3/2)x2
                    The vertex point happens at -b/2a = -450/ -3 = 150
                    The dimensions of the maximum area is 150 by 225 which yields an area of  33750 square feet.



7)  Number of passengers = (2000 - 200x)
     rate = (20 + 5x)
        x represents the number of nickels to increase the fare.

R(x) = (2000 - 200x)(20 + 5x)  = 40000 + 6000x - 1000x2
The maximum happens at -b/2a = -6000/-2000 = 3
Thus the rate should increase by 3 nickels or 15 cents, raising the rates to 35 cents



8) a)     x2(3x - 16) - 4(3x - 16) = 0
            (x2 - 4)(3x - 16) = 0
            (x - 2)(x + 2)(3x - 16) = 0
The zeros are:  2, -2, 16/3
 
    b)    Let y = x2
            y2 - 6y - 27 = 0
            (y - 9)(y + 3) = 0
            y = 9 or y = -3
            Substitute this into the top equation to find x
Thus x = 3, -3, 
 
 
    c)     2, 3, 1
 
 
    d)      2, -1, -1 + 2i, -1 - 2i


9)  a)  If 2 + 3i is a factor, so is 2 - 3i.  Using the imaginary roots, the sum = 4 and product = 13.  Thus,
                                                          (x - 4)(x2 - 4x + 13) =
                                                           x3 - 8x2 + 29x - 52
 
 
    b)  If 3 - 5i is a root, so is 3 + 5i.  The sum is 6 and the product = 34.  Thus, the equation is:
                                                          x2 - 6x + 34
 
 
    c)  The sum of the imaginary roots = 2 and the product = 2.
         The sum of the irrational roots = 4 and the product = 1
         Thus the equation is:  (x2 - 2x + 2)(x2 - 4x + 1)  Multiplying yields:
                                         x4 - 6x3 + 11x2 - 10x + 2


10)  a)  sum = -4/-2 = 2                      product = 7/2
 
 
       b)   sum = 3/4                             product = -2/4 = -1/2

  I aced this puppy!!  Get me out of here! 
  I bombed this test!!  Let me go back and study a little more!!