Deck 12: Polynomial Functions of Higher Degree

Question 1

Determine the number of turning points of the graph of the function.​ $$f ( x ) = 2 x ^ { 4 } + 4 x ^ { 2 } + 4$$ ​

A)Number of turning points: 3
B)Number of turning points: 1
C)Number of turning points: 5
D)Number of turning points: 2
E)Number of turning points: 4

Answer 1

Number of turning points: 1

Question 2

Find all the real zeros of the polynomial function and determine the multiplicity of each zero and the number of turning points of the graph of the function.​ $h ( t ) = t ^ { 2 } - 14 t + 49$ ​

A)All Real Zeros: 0, $7$ ;Even multiplicity;number of turning points: 2
B)All Real Zeros: $7$ ;Even multiplicity;number of turning points: 1
C)All Real Zeros: 0, $49$ ;Odd multiplicity;number of turning points: 2
D)All Real Zeros: 0,1, $7$ ;Even multiplicity;number of turning points: 3
E)All Real Zeros: $7$ ;Odd multiplicity;number of turning points: 1

Answer 2

All Real Zeros: $7$ ;Even multiplicity;number of turning points: 1

Question 3

Select from the following which is the polynomial function that has the given zeros.​ $$0 , - 7 , - 3$$ ​

A) $f ( x ) = - x ^ { 3 } + 10 x ^ { 2 } + 21 x$
B) $f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 21 x$
C) $f ( x ) = x ^ { 3 } + 10 x ^ { 2 } + 21 x$
D) $f ( x ) = x ^ { 3 } - 10 x ^ { 2 } - 21 x$
E) $f ( x ) = x ^ { 3 } + 10 x ^ { 2 } - 21 x$

Answer 3

$f ( x ) = x ^ { 3 } + 10 x ^ { 2 } + 21 x$

Question 4

Select the graph of $y = x ^ { 4 }$ and the transformation $f ( x ) = \left( \frac { 1 } { 2 } x \right) ^ { 4 } - 2$ . ​

A)​
B)​
C)​
D)​
E)​

Question 5

Select from the following which is the polynomial function that has the given zeros.​ $5 , - 7$ ​

A) $f ( x ) = x ^ { 2 } - 2 x + 35$
B) $f ( x ) = x ^ { 2 } + 2 x + 35$
C) $$f ( x ) = - x ^ { 2 } - 2 x - 35$$
D) $$f ( x ) = - x ^ { 2 } + 2 x - 35$$
E) $f ( x ) = x ^ { 2 } + 2 x - 35$

Question 6

Select the graph of $y = x ^ { 3 }$ and the transformation $$f ( x ) = ( x - 3 ) ^ { 3 }$$ . ​

A)​
B)​
C)​
D)​
E)​

Question 7

Select the correct graph of the function.​ $$f ( x ) = \frac { 1 } { 3 } x ^ { 2 } + \frac { 1 } { 3 } x - \frac { 8 } { 3 }$$ ​

A)​
B)​
C)​
D)​
E)​

Question 8

Select the graph of $y = x ^ { 6 }$ and the transformation $f ( x ) = ( x + 3 ) ^ { 6 }$ . ​

A)​
B)​
C)​
D)​
E)​

Question 9

Select the correct graph of the functions f and g which shows the right-hand and left-hand behaviors of f and g appear identical.​ $f ( x ) = - \left( 4 x ^ { 4 } - 3 x ^ { 3 } + 16 x \right)$ , $g ( x ) = - 4 x ^ { 4 }$ ​

A)​
B)​
C)​
D)​
E)​

Question 10

Select the correct description of right-hand and left-hand behavior of the graph of the polynomial function.​ $f ( x ) = \frac { 1 } { 2 } x ^ { 3 } + 3 x$ ​

A)Rises to the left,falls to the right
B)Rises to the right,rises to the left
C)Falls to the left,rises to the right
D)Falls to the right
E)Falls to the left,falls to the right

Question 11

Select the graph of $y = x ^ { 5 }$ and the transformation $f ( x ) = 1 - \frac { 1 } { 2 } x ^ { 5 }$ . ​

A)​
B)​
C)​
D)​
E)​

Question 12

Select the correct description of right-hand and left-hand behavior of the graph of the polynomial function.​ $$f ( x ) = 2 x ^ { 2 } - 3 x + 5$$ ​

A)Falls to the left,rises to the right
B)Falls to the left,falls to the right
C)Rises to the left,rises to the right
D)Rises to the left,falls to the right
E)Falls to the left

Question 13

Select the correct graph of the functions f and g in the same viewing window.Zoom out sufficiently far to show that the right-hand and left-hand behaviors of f and g appear identical.​ $f ( x ) = x ^ { 3 } - 4 x + 1$ , $g ( x ) = x ^ { 3 }$ ​

A)​
B)​
C)​
D)​
E)​

Question 14

Select the correct graph of the function.​ $$y = 2 x ^ { 3 } - 24 x ^ { 2 } + 36 x$$ ​

A)​
B)​
C)​
D)​
E)​

Question 15

Find all the real zeros of the polynomial function.​ $f ( x ) = x ^ { 2 } - 9$ ​

A) $- 9$
B) $$3$$
C) $$- 3$$
D) $9$
E) $\pm 3$

Question 16

Select from the following which is the polynomial function that has the given zeros.​ $$0,5$$ ​

A) $f ( x ) = x ^ { 2 } - 5 x$
B) $f ( x ) = x ^ { 3 } + x ^ { 2 } - 5 x$
C) $f ( x ) = x - 5$
D) $f ( x ) = x + 5$
E) $f ( x ) = x ^ { 2 } + 5 x$

Question 17

Select the correct description of right-hand and left-hand behavior of the graph of the polynomial function.​ $$f ( t ) = 2 - 5 x + 3 x ^ { 2 } - 5 x ^ { 3 }$$ ​

A)Falls to the left,falls to the right
B)Rises to the left,rises to the right
C)Rises to the left,falls to the right
D)Falls to the left,rises to the right
E)Falls to the left

Question 18

Select the correct description of right-hand and left-hand behavior of the graph of the polynomial function.​ $$f ( t ) = - \frac { 3 } { 5 } \left( t ^ { 2 } - 4 t + 5 \right)$$ ​

A)Rises to the left,rises to the right
B)Falls to the left,rises to the right
C)Falls to the left,falls to the right
D)Rises to the left,falls to the right
E)Rises to the left

Question 19

Select the correct graph of the function.​ $$y = x ^ { 5 } - 5 x ^ { 3 } + 3 x$$ ​

A)​
B)​
C)​
D)​
E)​

Question 20

Find all the real zeros of the polynomial function.​ $f ( x ) = x ^ { 5 } - 16 x ^ { 3 } + 64 x$ ​

A) $0 , \pm \sqrt { 8 }$
B) $0 , \sqrt { 8 }$
C) $0,8$
D) $0 , - 8$
E) $0 , - \sqrt { 8 }$

Question 21

Select from the following which is the polynomial function that has the given zeros.​ $1 + \sqrt { 5 } , 1 - \sqrt { 5 }$ ​

A) $f ( x ) = - x ^ { 2 } - 2 x - 4$
B) $f ( x ) = - x ^ { 2 } - 2 x + 4$ ​
C) $f ( x ) = x ^ { 2 } - 2 x - 4$
D) $f ( x ) = x ^ { 2 } - 2 x + 4$
E) $f ( x ) = x ^ { 2 } + 2 x - 4$

Question 22

Select the graph of the function and use the zero or root feature to approximate the real zeros of the function.​ $$f ( x ) = \frac { 1 } { 8 } x ^ { 4 } - 4 x ^ { 2 }$$ ​

A)​Zeros: $$0 , - 4 \sqrt { 2 }$$ ​
B)​Zeros: $$0 , \pm 4 \sqrt { 2 }$$ ​
C)​Zeros: $$0 , - 4 \sqrt { 2 }$$ ​
D)​Zeros: $$0 , \pm 4 \sqrt { 2 }$$ ​
E)​Zeros: $$0,4 \sqrt { 2 }$$ ​

Question 23

Select from the following which is the polynomial of degree n that has the given zero(s). ​
Zero
Degree $x = 3$ $n = 3$ ​
​

A) $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 27 x - 27$
B) $f ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 27 x - 27$
C) $f ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 27 x + 27$
D) $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 27 x + 27$
E) $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } - 27 x - 27$

Question 24

Select from the following which is the polynomial function that has the given zeros.​ $- 4 , - 2,0,2,4$ ​

A) $f ( x ) = x ^ { 5 } - 20 x ^ { 3 } + 64$
B) $f ( x ) = x ^ { 5 } + 20 x ^ { 3 } + 64 x$
C) $f ( x ) = x ^ { 5 } - 20 x ^ { 3 } + 64 x$
D) $f ( x ) = - x ^ { 5 } - 20 x ^ { 3 } + 64 x$
E) $f ( x ) = x ^ { 5 } - 20 x ^ { 3 } - 64 x$

Question 25

Select from the following which is the polynomial of degree n that has the given zero(s). ​
Zeros
Degree $x = 0 , \sqrt { 5 } , - \sqrt { 5 }$ $$n = 3$$ ​
​

A) $f ( x ) = x ^ { 3 } + \sqrt { 5 } x$
B) $f ( x ) = x ^ { 3 } + 5 x$
C) $f ( x ) = - x ^ { 3 } - 5 x$
D) $f ( x ) = x ^ { 3 } - \sqrt { 5 } x$
E) $f ( x ) = x ^ { 3 } - 5 x$

Question 26

Select the graph of the function and determine the zeros of the polynomial.​ $$g ( t ) = - \frac { 1 } { 4 } ( t - 2 ) ^ { 2 } ( t + 2 ) ^ { 2 }$$ ​

A)​ $$- 2$$ ​
B)​ $$2$$ ​
C)​ $$\pm 2$$ ​
D)​ $$2$$ ​
E)​ $$- 2$$ ​

Question 27

Select the graph of the function and use the zero or root feature to approximate the real zeros of the function.​ $$g ( x ) = \frac { 1 } { 5 } ( x + 1 ) ^ { 2 } ( x - 3 ) ( 2 x - 7 )$$ ​

A)​ Zeros: $$- 1,3 , \pm \frac { 7 } { 2 }$$
​
B)​ Zeros: $$- 1,3 , - \frac { 7 } { 2 }$$
​
C)​ Zeros: $$- 1 , \pm 3 , \frac { 7 } { 2 }$$
​
D)​ Zeros: $$- 1 , - 3 , \frac { 7 } { 2 }$$
​
E)​ Zeros: $$- 1,3 , \frac { 7 } { 2 }$$
​

Question 28

Select from the following which is the polynomial of degree n that has the given zero(s). ​
Zero
Degree $x = 0 , - 3$ $n = 5$ ​
​

A) $f ( x ) = x ^ { 5 } + 12 x ^ { 4 } + 54 x ^ { 3 } + 108 x ^ { 2 } + 81 x$
B) $f ( x ) = x ^ { 5 } - 12 x ^ { 4 } + 54 x ^ { 3 } + 108 x ^ { 2 } + 81 x$
C) $f ( x ) = x ^ { 5 } + 12 x ^ { 4 } + 54 x ^ { 3 } + 108 x ^ { 2 } - 81 x$
D) $f ( x ) = x ^ { 5 } + 12 x ^ { 4 } - 54 x ^ { 3 } + 108 x ^ { 2 } + 81 x$
E) $f ( x ) = x ^ { 5 } + 12 x ^ { 4 } + 54 x ^ { 3 } - 108 x ^ { 2 } + 81 x$

Question 29

An open box is to be made from a square piece of material,38 inches on a side,by cutting equal squares with sides of length x from the corners and turning up the sides (see figure)​ ​ where $a = 38 - 2 x$ .
Determine the domain of the following function,V(x)represents the volume of the box .​ $V ( x ) = x ( 38 - 2 x ) ^ { 2 }$ ​

A)Domain: $0 < x \leq 19$
B)Domain: $0 \leq x \leq 38$
C)Domain: $0 < x < 38$
D)Domain: $0 \leq x \leq 19$
E)Domain: $0 < x < 19$

Question 30

Select from the following which is the polynomial of degree n that has the given zero(s). ​
Zero
Degree $x = - 7$ $n = 2$ ​
​

A) $f ( x ) = x ^ { 2 } + 14 x + 49$
B) $f ( x ) = x ^ { 2 } - 14 x - 49$
C) $f ( x ) = - x ^ { 2 } + 14 x + 49$
D) $f ( x ) = x ^ { 2 } - 14 x + 49$
E) $f ( x ) = x ^ { 2 } + 14 x - 49$

Question 31

Select the graph of the function and determine the zeros of the polynomial.​ $f ( x ) = x ^ { 3 } - 25 x$ ​

A)​ $0,5 , - 5$ ​
B)​ $$0,5 , - 5$$ ​
C)​ $$0,5 , - 5$$ ​
D)​ $$5 , - 5$$ ​
E)​ $$5 , - 5$$ ​

Question 32

Select the graph of the function and determine the zeros of the polynomial.​ $$f ( t ) = \frac { 1 } { 6 } \left( t ^ { 2 } - 2 t + 20 \right)$$ ​

A)​ No zeros
​
​
B)​ No zeros
​
​
C)​ $$0,10 , - 10$$ ​
D)​ No zeros
​
E)​ $$10 , - 10$$ ​

Question 33

Match the equation with its graph.​ $\frac { 1 } { 20 } \left( x ^ { 5 } - x ^ { 4 } - 5 x ^ { 3 } - x ^ { 2 } - 6 x \right)$

A)
B)
C)
D)
E)

Question 34

Select the graph of the function and use the zero or root feature to approximate the real zeros of the function.​ $$f ( x ) = x ^ { 3 } - 4 x$$ ​

A)​Zeros: $$0 , - 2$$ ​
B)​Zeros: $$0 , - 2$$ ​
C)​Zeros: $$0,2$$ ​
D)​Zeros: $$0 , \pm 2$$ ​
E)​Zeros: $$0 , \pm 2$$ ​

Question 35

Select the graph of the function and determine the zeros of the polynomial.​ $$f ( x ) = x ^ { 2 } ( x - 5 )$$ ​

A)​ $$0,5 , - 5$$ ​
​
B)​ $$0,5$$ ​
C)​ $$0 , - 5$$ ​
D)​ $$0,5$$ ​
E)​ $$0 , - 5$$ ​

Question 36

Describe the right-hand and the left-hand behavior of the graph of $q ( x ) = - 5 x ^ { 4 } + 12 x ^ { 3 } + 13$ .

A)Because the degree is even and the leading coefficient is negative,the graph falls to the left and rises to the right.
B)Because the degree is even and the leading coefficient is negative,the graph rises to the left and falls to the right.
C)Because the degree is even and the leading coefficient is negative,the graph falls to the left and falls to the right.
D)Because the degree is odd and the leading coefficient is negative,the graph rises to the left and rises to the right.
E)Because the degree is even and the leading coefficient is negative,the graph rises to the left and rises to the right.

Question 37

A roofing contractor is fabricating gutters from $10$ -inch aluminum sheeting.The contractor plans to use an aluminum siding folding press to create the gutter by creasing equal lengths for the sidewalls (see figure). ​ where $a = 10 - 2 x$ Let x represent the height of the sidewall of the gutter.Write a function A that represents the
Cross-sectional area of the gutter.
​

A) $A = - 2 x ^ { 2 } + 10 x$
B) $A = 10 x ^ { 2 } - 2 x$
C) $A = - 10 x - 2 x ^ { 2 }$
D) $A = 2 x ^ { 2 } - 10 x$
E) $A = 2 x ^ { 2 } + 10 x$

Question 38

Sketch the graph of the function by finding the zeros of the polynomial,​ $$f ( x ) = 2 x ^ { 3 } - 10 x ^ { 2 } + 12 x$$ ​

A)​ ​0,2,3
​
B)​ ​0,2,-3
​
C)​ ​0,-2,3
​
D)​ ​0,2,3
​
E)​ ​0,-2,-3
​

Question 39

Select the graph of the function and determine the zeros of the polynomial.​ $$f ( x ) = x ^ { 3 } - 5 x ^ { 2 }$$ ​

A)​ $$0,5$$ ​
B)​ $$0 , - 5$$ ​
C)​ $$0,5$$ ​
D)​ $$0,5 , - 5$$ ​
E)​ $$0,5 , - 5$$ ​

Question 40

The growth of a red oak tree is approximated by the function ​​ $G = - 0.003 t ^ { 3 } + 0.137 t ^ { 2 } + 0.458 t - 0.839$ ​
Where G is the height of the tree (in feet)and t $( 2 \leq t \leq 34 )$ is its age (in years).
Select the correct graph of the function.
​

A)​ ​
B)​
C)​
D)​
E)​

Question 41

Find a polynomial with the given zeros.​ $1,1,7$ ​

A) $9 x ^ { 2 } + 15 x - 7$
B) $x ^ { 3 } + 9 x ^ { 2 } - 15 x + 7$
C) $15 x ^ { 3 } - 9 x ^ { 2 } + 15 x - 7$
D) $x ^ { 3 } - 9 x ^ { 2 } + 15 x - 7$
E)none of these

Question 42

Using a graphing utility,graph $f ( x ) = x ^ { 3 } - 4 x$ and approximate the zeros and their multiplicity.

A) $x = 0 , \text { multiplicity } 2 ; x = - 2 \text {, multiplicity } 1$
B) $x = 0 \text {, multiplicity } 1 ; x = 2 \text {, multiplicity } 1 ; x = - 2 \text {, multiplicity } 1$
C) $x = 0 , \text { multiplicity } 3$
D) $x = 0 , \text { multiplicity } 1 ; x = 2 , \text { multiplicity } 2$
E) $x = 2 , \text { multiplicity } 2 ; x = - 2 \text {, multiplicity } 1$

Question 43

An open box is to be made from a square piece of cardboard,22 inches on a side,by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below).If the volume of the box is represented by $V ( x ) = x ( 22 - 2 x ) ^ { 2 }$ ,determine the domain of $V ( x )$ .

A) $D = \{ x \mid 0 < x < 22 \}$
B) $D = \{ x \mid 0 < x < 11 \}$
C) $D = \{ x \mid x > 0 \}$
D) $D = \{ x \mid 44 < x < 88 \}$
E) $D = \{ x \mid 11 < x < 22 \}$

Question 44

Find a polynomial with the given zeros.​ $7,1$ ​

A) $x ^ { 2 } - 8 x + 7$
B) $x ^ { 2 } - 8 x + 8$
C) $x ^ { 2 } - 8 x - 7$
D) $8 x ^ { 2 } - x + 7$
E)none of these

Question 45

Graph the polynomial function.​ $y = - x ^ { 3 } + 3$ ​

A)
B)
C)
D)

Question 46

Well whether the function $y = x ^ { 5 } + 9 x ^ { 3 }$ is even or odd.If it is neither,so indicate. ​

A)even
B)odd
C)neither

Question 47

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } - 61 x ^ { 2 } + 900$ and determine the multiplicity of each.

A) $x = - 5 , \text { multiplicity } 2 ; x = - 6 , \text { multiplicity } 2$
B) $x = 25 , \text { multiplicity } 2 ; x = 36 \text {, multiplicity } 2$
C) $x = 5 , \text { multiplicity } 2 ; x = 6 , \text { multiplicity } 2$
D) $x = 25 , \text { multiplicity } 2 ; x = 6 , \text { multiplicity } 2$
E) $x = 5 \text {, multiplicity } 1 ; x = - 5 \text {, multiplicity } 1 ; x = 6 \text {, multiplicity } 1 ; x = - 6 \text {, multiplicity } 1$

Question 48

Find all real zeros of the polynomial $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 36 x - 108$ and determine the multiplicity of each.

A) $x = 6 , \text { multiplicity } 2 ; x = - 3 \text {, multiplicity } 1$
B) $x = 6 \text {, multiplicity } 1 ; x = - 6 \text {, multiplicity } 1 ; x = - 3 \text {, multiplicity } 1$
C) $x = - 3 \text {, multiplicity } 2 ; x = - 6 \text {, multiplicity } 1$
D) $x = - 6 \text {, multiplicity } 1 ; x = 3 \text {, multiplicity } 1 ; x = - 3 \text {, multiplicity } 1$
E) $x = - 3 \text {, multiplicity } 3$

Question 49

An open box is to be made from a square piece of cardboard,33 inches on a side,by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below).Determine the function,V,in terms of x,that represents the volume of the box.

A) $V ( x ) = - 4 x ^ { 3 } + 66 x ^ { 2 } - 33 x$
B) $V ( x ) = - 2 x ^ { 3 } + 33 x ^ { 2 }$
C) $V ( x ) = 4 x ^ { 3 } - 132 x ^ { 2 } + 1089 x$
D) $V ( x ) = - 4 x ^ { 3 } + 66 x ^ { 2 }$
E) $V ( x ) = 4 x ^ { 3 } - 66 x ^ { 2 } + 33 x$

Question 50

Using a graphing utility,graph $$f ( x ) = x ^ { 5 } - 14 x ^ { 4 } + 49 x ^ { 3 }$$ and approximate the zeros and their multiplicity.

A) $x = 0 , \text { multiplicity } 2 ; x = 7 , \text { multiplicity } 3$
B) $x = 0 , \text { multiplicity } 1 ; x = 7 , \text { multiplicity } 1 ; x = - 7 , \text { multiplicity } 1 ; x = \text { \#\# } \mathrm { b \#\#} = \mathrm { m } , \text { multiplicity } 1$
C) $x = 0 , \text { multiplicity } 3 ; x = 7 , \text { multiplicity } 2$
D) $x = 0 , \text { multiplicity } 3 ; x = - 7 , \text { multiplicity } 2$
E) $x = 0 \text {, multiplicity } 2 ; x = 7 \text {, multiplicity } 2 ; x = - 7 \text {, multiplicity } 1$

Question 51

Find all real zeros of the polynomial $$f ( x ) = x ^ { 4 } + 7 x ^ { 3 } + 6 x ^ { 2 }$$ and determine the multiplicity of each.

A) $$x = 0 \text {, multiplicity } 2 ; x = - 1 \text {, multiplicity } 1 ; x = - 6 \text {, multiplicity } 1$$
B) $x = 1 , \text { multiplicity } 2 ; x = 6 , \text { multiplicity } 2$
C) $x = 0 \text {, multiplicity } 2 ; x = 1 \text {, multiplicity } 1 ; x = 6 \text {, multiplicity } 1$
D) $x = - 1 , \text { multiplicity } 2 ; x = - 6 , \text { multiplicity } 2$
E) $x = 0 , \text { multiplicity } 1 ; x = 1 , \text { multiplicity } 1 ; x = - 1 , \text { multiplicity } 1 ; x = 6 \text {, multiplicity } 1$

Question 52

Find all real zeros of the polynomial $f ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 4 x - 20$ and determine the multiplicity of each.

A) $x = - 5 , \text { multiplicity } 2 ; x = - 2 \text {, multiplicity } 1$
B) $x = - 5 , \text { multiplicity } 3$
C) $x = 2 \text {, multiplicity } 1 ; x = - 2 \text {, multiplicity } 1 ; x = - 5 \text {, multiplicity } 1$
D) $x = - 2 \text {, multiplicity } 1 ; x = 5 \text {, multiplicity } 1 ; x = - 5 \text {, multiplicity } 1$
E) $x = 2 , \text { multiplicity } 2 ; x = - 5 , \text { multiplicity } 1$

Question 53

Graph the polynomial function.​ $$y = x ^ { 3 } + 5 x ^ { 2 }$$ ​

A)
B)
C)
D)

Question 54

Find a polynomial with the given zeros.​ $0,0,0 , \sqrt { 3 } , - \sqrt { 3 }$ ​

A) $x ^ { 5 } - 3 x ^ { 3 }$
B) $x ^ { 5 } - 6 x ^ { 3 }$
C) $x ^ { 5 } - x ^ { 3 } + 3$
D) $x ^ { 2 } + 3 x + 6$
E)none of these

Question 55

Find a polynomial with the given zeros.​ $- 1,5 , - \sqrt { 7 } , \sqrt { 7 }$ ​

A) $x ^ { 5 } - 4 x ^ { 4 } - 12 x ^ { 3 } + 28 x ^ { 2 } + 35 x - 2$
B) $x ^ { 4 } - 12 x ^ { 2 } + 35$
C) $x ^ { 4 } - 12 x ^ { 3 } - 4 x ^ { 2 } - 28 x + 35$
D) $x ^ { 4 } - 4 x ^ { 3 } - 12 x ^ { 2 } + 28 x + 35$
E)none of these

Question 56

The graph of the function g(x)is a translation of the graph of f (x)= x ³.Graph the function g(x)= (x - 1)³. ​

A)​
B)​
C)​
D)​

Question 57

The graph of the function g(x)is a translation of the graph of f (x)= x ³.Graph the function g(x)= (x - 3)³ - 1. ​

A)
B)
C)
D)

Question 58

Describe the right-hand and the left-hand behavior of the graph of $s ( x ) = 3 x ^ { 5 } + 12 x ^ { 3 } + 3$ .

A)Because the degree is odd and the leading and the second coefficients are positive,the graph falls to the left and rises to the right.
B)Because the degree is odd,the leading and the second coefficient are positive,the graph rises to the left and rises to the right.
C)Because the degree is odd,and the leading coefficient is positive,the graph falls to the left and falls to the right.
D)Because the degree is odd,and the leading coefficient is positive,the graph rises to the left and falls to the right.
E)Because the degree is even and the leading coefficient is positive,the graph rises to the left and rises to the right.

Question 59

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 12 x ^ { 3 } + 27 x ^ { 2 }$ and determine the multiplicity of each.

A) $x = 0 \text {, multiplicity } 1 ; x = 9 , \text { multiplicity } 1 ; x = - 9 , \text { multiplicity } 1 ; x = 3 \text {, multiplicity } 1$
B) $x = 0 \text {, multiplicity } 2 ; x = 9 \text {, multiplicity } 1 ; x = 3 \text {, multiplicity } 1$
C) $x = 0 \text {, multiplicity } 2 ; x = - 9 \text {, multiplicity } 1 ; x = - 3 \text {, multiplicity } 1$
D) $x = 9 , \text { multiplicity } 2 ; x = 3 , \text { multiplicity } 2$

Question 60

Describe the right-hand and the left-hand behavior of the graph of $q ( x ) = - \frac { 7 } { 12 } \left( x ^ { 3 } - x ^ { 2 } + 2 x + 1 \right)$ .

A)Because the degree is odd and the leading coefficient is negative,the graph rises to the left and falls to the right.
B)Because the degree is odd and the leading coefficient is negative,the graph falls to the left and rises to the right.
C)Because the degree is odd and the leading coefficient is positive,the graph falls to the left and falls to the right.
D)Because the degree is odd and the leading coefficient is positive,the graph rises to the left and rises to the right.
E)Because the degree is even and the leading coefficient is negative,the graph rises to the left and falls to the right.

Question 61

An open box is to be made from a square piece of cardboard,24 inches on a side,by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below).If the volume of the box is represented by $V ( x ) = x ( 24 - 2 x ) ^ { 2 }$ ,determine the domain of $V ( x )$ .

A) $D = \{ x \mid x > 0 \}$
B) $$D = \{ x \mid 0 < x < 12 \}$$
C) $D = \{ x \mid 48 < x < 96 \}$
D) $D = \{ x \mid 0 < x < 24 \}$
E) $D = \{ x \mid 12 < x < 24 \}$

Question 62

An open box is to be made from a square piece of cardboard,28 inches on a side,by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below).Determine the function,V,in terms of x,that represents the volume of the box.

A) $V ( x ) = - 2 x ^ { 3 } + 28 x ^ { 2 }$
B) $V ( x ) = - 4 x ^ { 3 } + 56 x ^ { 2 }$
C) $V ( x ) = 4 x ^ { 3 } - 56 x ^ { 2 } + 28 x$
D) $V ( x ) = - 4 x ^ { 3 } + 56 x ^ { 2 } - 28 x$
E) $V ( x ) = 4 x ^ { 3 } - 112 x ^ { 2 } + 784 x$

Question 63

An open box is to be made from a square piece of cardboard, $66 \text { inches }$ on a side,by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below).After determining the function V,in terms of x,that represents the volume of the box,use a graphing utility to estimate the dimensions that will maximize its volume.

A) $22 ^ { \prime \prime } \times 22 ^ { \prime \prime } \times 11 ^ { \prime \prime }$
B) $44 ^ { \prime \prime } \times 44 ^ { \prime \prime } \times 11 ^ { \prime \prime }$
C) $44 ^ { \prime \prime } \times 44 ^ { \prime \prime } \times 22 ^ { \prime \prime }$
D) $33 ^ { \prime \prime } \times 33 ^ { \prime \prime } \times 22 ^ { \prime \prime }$
E) $11 ^ { \prime \prime } \times 11 ^ { \prime \prime } \times 5.5 ^ { \prime \prime }$