AnswersTX-Precalculus A-CRPolynomial Inequalities

Polynomial Inequalities Answers

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A ski lift is modeled by the function f(x) = (0.2)(–2x 3 + 23x 2 + 25x + 50), where x is the time in seconds. When it comes out of the first stop, it is now climbing toward its highest point from the ground.During which time interval will the ski lift reach a height over 50 feet above the ground?

A
0 < x < 2.7
B
0 < x < 11.8
C
2.7 < x < 11.8
D
11.8 < x < 12.6
2
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A store sells bouquets of fruits for $10 a bouquet. The daily cost to produce x bouquets of fruits is defined by the function f(x) = – x 4 + 3x 3 + 5x 2 + 20x + 1.What is the least number of bouquets that must be sold for the store to make a profit?

A
3
B
4
C
5
D
6
3

The width of a rectangular prism is five less than the length, and the height of the prism is twice the length. Let x represent the length of the prism.For what values of x will the volume of the rectangular prism be 500 cubic units or greater?

A
x < 8.5 units
B
x > 8.5 units
C
x ≤ 8.5 units
D
x ≥ 8.5 units
4

At a certain company, the monthly salary of project managers can be modeled by the function f(x) = x4 – 10x 2 + 10,000, where x is the number of years of employment.After how many years would a project manager be eligible for a $20,000 monthly salary?

A
after working for exactly 10 years
B
after working for at least 10 1/4 years
C
after working for exactly 12 years
D
after working for at least 12 1/4 years
5

The graph of f(x) = (0.2)(x4 + x3 – 12x2) is shown.

Question illustration
A
(–4, 0) U (0, 3)
B
[–4, 0) U (0, 3]
C
(–ꝏ, –4) U (3, ꝏ)
D
(–ꝏ, –4] U [3, ꝏ)
6

What is the solution to (x – 5)(x + 2)(x – 7) < 0?

A
A number line going from negative 8 to 8. Open circles are at negative 2, 5, and 7. The line is shaded to the left of negative 2 and between 5 and 7.
Option A
B
A number line going from negative 8 to 8. Open circles are at negative 2, 5, and 7. The line is shaded between negative 2 and 5 and to the right of 7.
Option B
C
A number line going from negative 8 to 8. Closed circles are at negative 2, 5, and 7. The line is shaded to the left of negative 2 and between 5 and 7.
Option C
D
Option
Option D
7

An aquarium has dimensions 2x feet, (x – 1) feet, and (x + 2) feet. The aquarium volume must be no more than 280 cubic feet.What are the possible values of x?

A
(1, 5)
B
(1, 5]
C
[1, 5)
D
[1, 5]
8

What is the solution to x 4 – 12x 2 + 10 > 0?

A
(–0.95, 0.95)
B
(–3.33, 3.33)
C
(–3.33, –0.95) U (0.95, 3.33)
D
(–ꝏ, –3.33) U (–0.95, 0.95) U (3.33, ꝏ)
10

What is the solution to (x – 5)(2x + 1)(x – 7) > 0?

A
(–0.5, 5) U (7, ꝏ)
B
(–ꝏ, –0.5) U (5, 7)
C
(–0.5, 5] U [7, ꝏ)
D
(–ꝏ, –0.5] U [5, 7]
11

What is the solution to x 3 + x 2 ≤ 10x – 8?

A
{–4, 1, 2}
B
(–ꝏ, –4]
C
(–ꝏ, –4) U [1, 2]
D
(–ꝏ, –4] U [1, 2]
12

The cube of a number is less than five times the square of the number. For what set of numbers is this true?

A
(–ꝏ, 5)
B
(5, ꝏ)
C
(–ꝏ, 0) U (0, 5)
D
(–ꝏ, 5) U (5, ꝏ)
13

You are building a rectangular garden against the back of your house, using 80 feet of fencing. The area of the garden needs to be greater than 400 square feet but less than 600 square feet.

Question illustration
A
Option
Option A
B
(20 minus 10 StartRoot 2 EndRoot, 20 + 10 StartRoot 2 EndRoot)
Option B
C
Option
Option C
D
Option
Option D
14

Consider the graph of f(x) = 2x 3 – 3x 2 – 14x.

Question illustration
A
–2 < x < 0 or 3.5 < x < ꝏ
B
–2 < x < 0 or 3.5 ≤ x ≤ ꝏ
C
–2 ≤ x ≤ 0 or 3.5 ≤ x ≤ ꝏ
D
–2 ≤ x ≤ 0 or 3.5 ≤ x < ꝏ
15

What is the solution to (x + 2)(x – 3)2 > 0?

A
A number line going from negative 4 to 4. The entire line is shaded with arrows going left and right.
Option A
B
A number line going from negative 4 to 4. An open circle is at negative 2. The line is shaded to the right of negative 2.
Option B
C
A number line going from negative 4 to 4. Open circles are at negative 2 and 3. The line is shaded between negative 2 and 3.
Option C
D
A number line going from negative 4 to 4. Open circles are at negative 2 and 3. The line is shaded to the right of negative 2.
Option D
16

What are the minimum and maximum values of x, for which x3 + x2 – 6x ≥ 0?

A
minimum = –3, maximum = 0
B
minimum = 0, maximum = 2
C
minimum = –3, no maximum
D
minimum = 2, no maximum
17

What is the solution to x6 – 6x 5 + 15x 4 – 20x 3 + 15x 2 – 6x + 1 ≥ 0?

A
x = 0
B
x = 1
C
all real numbers
D
all real numbers except zero

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