 Working with Polynomials Terms of Use    Contact Person: Donna Roberts  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 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. 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. 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 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) 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) 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 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 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)→ ∞ 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:     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 