Practice Page
Directions: Answer these questions involving polynomials. Check each answer when finished.

1.
The length of the rectangle at the right is
3x + 6, and the area is 6x2 + 3x - 18. What expression represents the width (?) of the rectangle?
Choose:
3x - 2
2x + 3
3x - 3
2x - 3

work1

 

 

2.
The polynomial function P(x) = -x4 + 9x3 - 23x2 +15x, on the interval from x = 0 to x = 6, represents six month profits of a new commercial web site. The equation y = 0 represents break-even.
dollar
 
a) During this time period, when did the company experience break-even?
Choose:
x = 0,1,3,5
x = 1,±3,5
x = ±1,3,5
x = 1,3,4,5
 

b) During this time period, on what interval was the company in the red (losing money)? (Note: Choices are expressed in interval notation.)
Choose:
(0,1), (3,5)
(1,3)
(1,3), (5,6]
(3,5)

 

 

3.
The polynomial functions f (x) = x3 + 3x2 - 3x - 1 and g(x) = x2 + 9 represent two mapped winding paths through Carlsbad Park.
  At what x-value(s) on the map will the two paths intersect?

 Choose:
x = 2 x = ±2
x = 2 and 4 x = 2 and 40
The paths do not intersect.
hiker

 

 

4.
Rectangle ABCD is congruent to rectangle EFGH. The area of rectangle ABCD is expressed as x2 + 6x + 8 and the area of rectangle EFGH is expressed as k + (x + 3)2 - 9.
 
What is the value of k?
Choose:
k = 2 k = 4
k = 8
k = 9
work2

 

 

5.
Regarding the graph shown below, which of the equations represents the graph?
 
Choose:
P(x) = 0.5(x - 2)(x + 1)(x + 4)
P(x) = 0.25(x - 2)(x + 1)(x + 4)
P(x) = 0.5(x + 2)(x - 1)(x - 4)
P(x) = 0.25(x + 2)(x - 1)(x - 4)
polygraph5

 

 

6.
A designer has hollowed out a block of wood as shown. Which of the following polynomials represents the volume of the remaining (blue) figure?
Choose:
2x3 + 15x2 + 33x + 12
(x + 4)(2x + 1)(x + 3) - (2x - 3)(x)
12x2 + 40x + 12
(x + 3)(x + 4)(2x + 1)
poly6pic
Rectangular solid with a rectangular solid hollowed out of the center.

 

 

7.
The graph of y = x3 - 4x2 + x + 6 is shown at the right.
Which of the following choices is the product of the roots of this equation?

Choose:
4
6
-6
-36
workpoly8

 

 

8.
You are given the polynomial function
P(x) = 6x3 + kx2 - 52x + 15. You know that one of the roots is x = 1.5.
a) What is the value of k?
Choose:
11
13
19
22

b) What are the zeros of P(x)?
Choose:
1/3, 1.5, -5 -1/3, 1.5, 5
1, 1.5, -5 -1, 1.5, 5
work8

 

 

9.
Which of the following statements are TRUE regarding the polynomial function shown below?
(Check all that apply, and hit SUBMIT!)
 

(x - 3) is a factor

-2 is a root

as x → -∞, f(x)→ -∞

the degree is 3

(x - 0) repeated factor

maximum at x = 2

as x →∞, f(x)→ ∞

        

work9

 

 

10.
The diagram shown below is a right, rectangular solid with a height expressed as x - 1. The polynomial function P(x) = m2x3 - 6mx + 9 represents the volume of the solid based upon positive values of x.
 
a) Assuming m to be a constant, find m.
Choose:
m = 1
m = 2
m = 3
m = 4

b) What roots of P(x) fall on the positive x-axis?
Choose:
workm4
workm3
workm1
workm2
work3
 

c) What interval(s), on the positive x-axis, cannot represent the volume of the solid?
Choose:
(Choices are expressed in interval notation to nearest hundredths.)
[0.62, 0]
(0, 1]
[0, 0.62], [1, ∞)
[-1.62, 0.62]

d) If the domain of P(x) is given to be 1 < x < 20, find the maximum volume of the solid on this domain, in cubic units.
Choose:
9 cu. units
18.798 cu. units
8829 cu. units
71649 cu. units

 

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