Sample test for chapter two!!
 
 
Hope your aim is good!!
 
 
1)  Use synthetic substitution to find each value for P(x) = 4x3 - 3x2 +5.
            a) P(-2)                b) P(3)            c)  P(1/2)                d)  P(-1/2)
 
 
2)  The leading coefficient of a cubic polynomial is 2, and the coefficient of the linear term is -5.  If P(0) = 7 and P(2) = 21, find P(-1).
 
 
3)  Find the remainder when x5 - 3x3 + x2 - 3 is divided by:
                a)  x - 1                b)  x - 2                c)  x + 1                d)  x + 2
 
 
4)  Find the remaining factors for x4 - 10x3 + 35x2 - 50x + 24 if two factors are x - 1, and x - 3.
 
 
5)  Sketch the graph of each of the following equations.  Note what happens at double and triple roots.
                a)  y = (x - 1)(x + 3)(x - 2)                    b)  y = x2(x + 5)(x - 2)
                c)  y = (x - 1)3                                       d)  y = x3(x - 1)2
 
 
6)  There are 900 feet of fencing available to enclose a rectangular plot with a fence down the middle and parallel to two ends.  What is the maximum area which can be enclosed?
 
 
7)  A bus line carries 2000 passengers per day at a rate of 20 cents per passenger.  Management wants to make a rate change, and they estimate they would lose 200 passengers for every 5 cent increase.  What rate should they charge to maximize the revenue?
 
 
8) Solve each equation by the stated method:
 
            a)  grouping method.   3x3 - 16x2 - 12x + 64 = 0
 
            b)  Quadratic form.     x4 - 6x2 - 27 = 0
 
            c)  Rational root theorem.     x3 - 6x2 + 11x - 6 = 0
                                                           x4 + x3 + x2 - 9x - 10 = 0
 
 
9)  Find each type of equation with the given roots.
 
                a)  cubic equation with  4,  2 + 3i
 
                b)  quadratic equation with   3 - 5i
 
                c)  quartic equation with 
 
 
10)  State the sum and product of the roots of each equation.
 
                a)  2x2 - 4x + 7 = 0                            b)  4x3 - 3x2 - 5x + 2 = 0
 

 
  On to the answers: 
  Take me back, I biffed: