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
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