
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 6x^{2} + 3x  18. What expression represents the width (?) of the rectangle?
Choose:



2. 
The polynomial function P(x) = x^{4} + 9x^{3}  23x^{2} +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 breakeven. 


a) During this time period, when did the company experience breakeven?
Choose:


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


3. 
The polynomial functions f (x) = x^{3} + 3x^{2}  3x  1 and g(x) = x^{2} + 9 represent two mapped winding paths through Carlsbad Park. 

At what xvalue(s) on the map will the two paths intersect?
Choose:



4. 
Rectangle ABCD is congruent to rectangle EFGH. The area of rectangle ABCD is expressed as x^{2} + 6x + 8 and the area of rectangle EFGH is expressed as k + (x + 3)^{2 } 9.


What is the value of k?
Choose:



5. 
Regarding the graph shown below, which of the equations represents the graph?


Choose:



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:

Rectangular solid with a rectangular solid hollowed out of the center. 

7. 
The graph of y = x^{3}  4x^{2} + x + 6 is shown at the right.
Which of the following choices is the product of the roots of this equation?
Choose:



8. 
You are given the polynomial function
P(x) =
6x^{3} + kx^{2}  52x + 15. You know that one of the roots is x = 1.5.
a) What is the value of k?
Choose:
b) What are the zeros of P(x)?
Choose:



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



10. 
The diagram shown below is a right, rectangular solid with a height expressed as x  1. The polynomial function P(x) = m^{2}x^{3}  6mx + 9 represents the volume of the solid based upon positive values of x. 

a) Assuming m to be a constant, find m.
Choose:
b) What roots of P(x) fall on the positive xaxis?
Choose:



c) What interval(s), on the positive xaxis, cannot represent the volume of the solid?
Choose:
(Choices are expressed in interval notation to nearest hundredths.)
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:


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