Question 1

Use synthetic division to perform the division.
-$$\frac { x ^ { 4 } - 2 x ^ { 3 } - 13 x ^ { 2 } - 8 x - 10 } { x - 5 }$$

Accepted Answer

A)  $x ^ { 3 } + 3 x ^ { 2 } + 2 x + 2$ 
B)  $x ^ { 3 } + 4 x ^ { 2 } + 2 x - 2$ 
C)  $x ^ { 3 } + 3 x ^ { 2 } + 4 x$ 
D)  $x ^ { 3 } + 3 x ^ { 2 } + 4 x + 4$ 
A)  $x ^ { 3 } + 3 x ^ { 2 } + 2 x + 2$ 
B)  $x ^ { 3 } + 4 x ^ { 2 } + 2 x - 2$ 
C)  $x ^ { 3 } + 3 x ^ { 2 } + 4 x$ 
D)  $x ^ { 3 } + 3 x ^ { 2 } + 4 x + 4$

Question 2

A piece of cardboard is twice as long as it is wide. It is to be made into a box with an open top by cutting 2 cm squares from each corner and folding up the sides. Let x represent the width of the original piece of cardboard.
Find the width of the original piece of cardboard, x, if the volume of the box is $2496 \mathrm {~cm} ^ { 3 }$ .

Accepted Answer

A)  27 cm 
B)  29 cm 
C)  24 cm 
D)  28 cm 
A)  27 cm 
B)  29 cm 
C)  24 cm 
D)  28 cm

Question 3

Provide an appropriate response.
-Explain the behavior of the graph of $f ( x )$ as it approaches its vertical asymptote. $f ( x ) = \frac { - 1 } { ( x - 6 ) ^ { 2 } }$

Accepted Answer

A)  Approaches $\infty$ from the left and the right 
B)  Approaches $\infty$ from the left, approaches $- \infty$ from the right 
C)  Approaches $- \infty$ from the left and the right 
D)  Approaches $- \infty$ from the left, approaches $\infty$ from the right 
A)  Approaches $\infty$ from the left and the right 
B)  Approaches $\infty$ from the left, approaches $- \infty$ from the right 
C)  Approaches $- \infty$ from the left and the right 
D)  Approaches $- \infty$ from the left, approaches $\infty$ from the right

Question 4

Find a polynomial of least degree with only real coefficients and having the given zeros.
-$- \sqrt { 3 } , \sqrt { 3 }$, and $- 4 \mathrm { i }$

Accepted Answer

A)  $f ( x ) = x ^ { 4 } + 13 x ^ { 2 } - 48$ 
B)  $f ( x ) = x ^ { 4 } + 26 x ^ { 2 } + 48$ 
C)  $f ( x ) = x ^ { 4 } - 26 x ^ { 2 } + 48$ 
D)  $f ( x ) = x ^ { 4 } - 13 x ^ { 2 } - 48$ 
A)  $f ( x ) = x ^ { 4 } + 13 x ^ { 2 } - 48$ 
B)  $f ( x ) = x ^ { 4 } + 26 x ^ { 2 } + 48$ 
C)  $f ( x ) = x ^ { 4 } - 26 x ^ { 2 } + 48$ 
D)  $f ( x ) = x ^ { 4 } - 13 x ^ { 2 } - 48$

Question 5

If  m  varies directly as  x  and  y , and  m=24  when  x=6  and  y=9 , find  m  when  x=15  and  y=8 .

Accepted Answer

A)  $\frac { 64 } { 3 }$ 
B)  60 
C)  $\frac { 140 } { 3 }$ 
D)  $\frac { 160 } { 3 }$ 
A)  $\frac { 64 } { 3 }$ 
B)  60 
C)  $\frac { 140 } { 3 }$ 
D)  $\frac { 160 } { 3 }$

Question 6

If an object is propelled upward from a height of 144 feet at an initial velocity of 128 feet per second, then its height after t seconds is given by the equation $h ( t ) = - 16 t ^ { 2 } + 128 t + 144$ After how many seconds does the object
Hit the ground?

Accepted Answer

A)  9 sec 
B)  8.0 sec 
C)  11 sec 
D)  4.5 sec 
A)  9 sec 
B)  8.0 sec 
C)  11 sec 
D)  4.5 sec

Question 7

Sketch the graph of the rational function.
-$$f ( x ) = \frac { ( x - 3 ) ( x - 1 ) } { ( x - 2 ) ^ { 2 } }$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 8

Factor f(x) into linear factors given that k is a zero of f(x).
-$$f ( x ) = 10 x ^ { 3 } + 53 x ^ { 2 } + 49 x - 12 ; k = \frac { 1 } { 5 }$$

Accepted Answer

A)  $( 5 x + 1 ) ( 2 x + 3 ) ( x - 4 )$ 
B)  $( 5 x - 1 ) ( 2 x + 3 ) ( x + 4 )$ 
C)  $( 5 x - 1 ) ( 2 x - 3 ) ( x - 4 )$ 
D)  $( 5 x + 1 ) ( 2 x + 1 ) ( x - 12 )$ 
A)  $( 5 x + 1 ) ( 2 x + 3 ) ( x - 4 )$ 
B)  $( 5 x - 1 ) ( 2 x + 3 ) ( x + 4 )$ 
C)  $( 5 x - 1 ) ( 2 x - 3 ) ( x - 4 )$ 
D)  $( 5 x + 1 ) ( 2 x + 1 ) ( x - 12 )$

Question 9

Translate the given formula to an English phrase using the word "varies".
-$\mathrm { f } - \mathrm { stop } = \frac { \mathrm { f } } { \mathrm { D } }$ , where f-stop is camera setting with a lens with focal length f and diaphragm opening D

Accepted Answer

A camera's f-stop va

Question 10

Provide an appropriate response.
-For what value of $c$ does the quadratic function $f ( x ) = x ^ { 2 } - 6 x + c$ have exactly one $x$-intercept?

Accepted Answer

A)  9 
B)  $- 9$ 
C)  24 
D)  $\frac { 3 } { 2 }$ 
A)  9 
B)  $- 9$ 
C)  24 
D)  $\frac { 3 } { 2 }$

Question 11

Determine whether the statement is true or false.
-$$\text { The function } f ( x ) = \frac { 2 - x ^ { 2 } } { x ^ { 2 } + 5 } \text { has a horizontal asymptote of } y = - 1 \text {. }$$

Accepted Answer

A) True 
 B)False

Question 12

Find the correct end behavior diagram for the given polynomial function.
-$$P ( x ) = - 2 x ^ { 6 } + 7 x ^ { 5 } - x ^ { 2 } - 2 x + 4$$

Accepted Answer

A)   
B)    
C)    
D)    
A)   
B)    
C)    
D)

Question 13

Solve the inequality. Write the solution set in interval notation.
-$$3 x ^ { 2 } + 14 x < 24$$

Accepted Answer

A)  $\left( -\infty , - \frac { 4 } { 3 } \right) \cup ( 6 , \infty )$ 
B)  $\left( - 6 , \frac { 4 } { 3 } \right)$ 
C)  $ \left( - \frac { 4 } { 3 } , 6 \right)$ 
D)  $( -\infty , - 6 ) \cup \left( \frac { 4 } { 3 } , \infty \right)$ 
A)  $\left( -\infty , - \frac { 4 } { 3 } \right) \cup ( 6 , \infty )$ 
B)  $\left( - 6 , \frac { 4 } { 3 } \right)$ 
C)  $ \left( - \frac { 4 } { 3 } , 6 \right)$ 
D)  $( -\infty , - 6 ) \cup \left( \frac { 4 } { 3 } , \infty \right)$

Question 14

Give the equations of any horizontal asymptotes.
-$$h ( x ) = \frac { 7 x ^ { 2 } - 9 x - 6 } { 3 x ^ { 2 } - 4 x + 7 }$$

Accepted Answer

A)  $y = \frac { 9 } { 4 }$ 
B)  none 
C)  $y = 0$ 
D)  $y = \frac { 7 } { 3 }$ 
A)  $y = \frac { 9 } { 4 }$ 
B)  none 
C)  $y = 0$ 
D)  $y = \frac { 7 } { 3 }$

Question 15

Use synthetic division to decide whether the given number k is a zero of the given polynomial function.
-$k = - 2 ; f ( x ) = - 8 x ^ { 3 } - 9 x ^ { 2 } + x - 26$

Accepted Answer

A) True 
 B)False

Question 16

Find a polynomial function f(x) of least possible degree having the graph shown.
-

Accepted Answer

A)  $f ( x ) = \frac { 1 } { 3 } ( x + 2 ) ( x - 3 ) ^ { 2 }$ 
B)  $f ( x ) = \frac { 1 } { 3 } ( x - 2 ) ( x + 3 )$ 
C)  $f ( x ) = \frac { 1 } { 3 } ( x - 2 ) ( x + 3 ) ^ { 2 }$ 
D)  $f ( x ) = \frac { 1 } { 3 } ( x + 2 ) ( x - 3 )$ 
A)  $f ( x ) = \frac { 1 } { 3 } ( x + 2 ) ( x - 3 ) ^ { 2 }$ 
B)  $f ( x ) = \frac { 1 } { 3 } ( x - 2 ) ( x + 3 )$ 
C)  $f ( x ) = \frac { 1 } { 3 } ( x - 2 ) ( x + 3 ) ^ { 2 }$ 
D)  $f ( x ) = \frac { 1 } { 3 } ( x + 2 ) ( x - 3 )$

Question 17

Solve the problem. Round your answer to two decimal places.
-The distance an object falls when dropped from a tower varies directly as the square of the time it falls. If the object falls 144 feet in 3 seconds, how far will it fall in 15 seconds?

Accepted Answer

A)  3150 ft 
B)  240 ft 
C)  3600 ft 
D)  4050 ft 
A)  3150 ft 
B)  240 ft 
C)  3600 ft 
D)  4050 ft

Question 18

Provide an appropriate response.
-For what value of $c$ does the quadratic function $f ( x ) = 3 x ^ { 2 } + 8 x + c$ have exactly one $x$-intercept?

Accepted Answer

A)  $- \frac { 2 } { 3 }$ 
B)  $\frac { 16 } { 3 }$ 
C)  $\frac { 2 } { 3 }$ 
D)  16 
A)  $- \frac { 2 } { 3 }$ 
B)  $\frac { 16 } { 3 }$ 
C)  $\frac { 2 } { 3 }$ 
D)  16

Question 19

Graph the polynomial function. Factor first if the expression is not in factored form.
-$f(x)=x\left(x^{2}-9\right)(x+1)^{3}$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 20

A toy rocket is shot vertically upward from the ground. Its distance in feet from the ground in $t$ seconds is given by $s ( t ) = - 16 \left( t ^ { 2 } \right) + 175 t$. At what time(s) will the ball be $162 \mathrm { ft }$ from the ground? Round your answer to the nearest tenth of a second.

Accepted Answer

A)  169.8 sec and 180.2 sec 
B)  5.5 sec 
C)  10.9 sec 
D)  1.0 sec and 9.9 sec 
A)  169.8 sec and 180.2 sec 
B)  5.5 sec 
C)  10.9 sec 
D)  1.0 sec and 9.9 sec

Use synthetic division to perform the division. - $\frac { x ^ { 4 } - 2 x ^ { 3 } - 13 x ^ { 2 } - 8 x - 10 } { x - 5 }$

Provide an appropriate response. -Explain the behavior of the graph of $f ( x )$ as it approaches its vertical asymptote. $f ( x ) = \frac { - 1 } { ( x - 6 ) ^ { 2 } }$

Find a polynomial of least degree with only real coefficients and having the given zeros. - $- \sqrt { 3 } , \sqrt { 3 }$ , and $- 4 \mathrm { i }$

If m varies directly as x and y , and m=24 when x=6 and y=9 , find m when x=15 and y=8 .

If an object is propelled upward from a height of 144 feet at an initial velocity of 128 feet per second, then its height after t seconds is given by the equation $h ( t ) = - 16 t ^ { 2 } + 128 t + 144$ After how many seconds does the object Hit the ground?

Sketch the graph of the rational function. - $f ( x ) = \frac { ( x - 3 ) ( x - 1 ) } { ( x - 2 ) ^ { 2 } }$ $Sketch the graph of the rational function. - f ( x ) = \frac { ( x - 3 ) ( x - 1 ) } { ( x - 2 ) ^ { 2 } }$

Factor f(x) into linear factors given that k is a zero of f(x). - $f ( x ) = 10 x ^ { 3 } + 53 x ^ { 2 } + 49 x - 12 ; k = \frac { 1 } { 5 }$

Translate the given formula to an English phrase using the word "varies". - $\mathrm { f } - \mathrm { stop } = \frac { \mathrm { f } } { \mathrm { D } }$ , where f-stop is camera setting with a lens with focal length f and diaphragm opening D

Provide an appropriate response. -For what value of $c$ does the quadratic function $f ( x ) = x ^ { 2 } - 6 x + c$ have exactly one $x$ -intercept?

Determine whether the statement is true or false. - $\text { The function } f ( x ) = \frac { 2 - x ^ { 2 } } { x ^ { 2 } + 5 } \text { has a horizontal asymptote of } y = - 1 \text {. }$

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = - 2 x ^ { 6 } + 7 x ^ { 5 } - x ^ { 2 } - 2 x + 4$

Solve the inequality. Write the solution set in interval notation. - $3 x ^ { 2 } + 14 x < 24$

Give the equations of any horizontal asymptotes. - $h ( x ) = \frac { 7 x ^ { 2 } - 9 x - 6 } { 3 x ^ { 2 } - 4 x + 7 }$

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = - 2 ; f ( x ) = - 8 x ^ { 3 } - 9 x ^ { 2 } + x - 26$

Find a polynomial function f(x) of least possible degree having the graph shown. -

Solve the problem. Round your answer to two decimal places. -The distance an object falls when dropped from a tower varies directly as the square of the time it falls. If the object falls 144 feet in 3 seconds, how far will it fall in 15 seconds?

Provide an appropriate response. -For what value of $c$ does the quadratic function $f ( x ) = 3 x ^ { 2 } + 8 x + c$ have exactly one $x$ -intercept?

Graph the polynomial function. Factor first if the expression is not in factored form. - $f(x)=x\left(x^{2}-9\right)(x+1)^{3}$ $Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=x\left(x^{2}-9\right)(x+1)^{3}$

A toy rocket is shot vertically upward from the ground. Its distance in feet from the ground in $t$ seconds is given by $s ( t ) = - 16 \left( t ^ { 2 } \right) + 175 t$ . At what time(s) will the ball be $162 \mathrm { ft }$ from the ground? Round your answer to the nearest tenth of a second.

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 4: Polynomials and Rational Functions

Use synthetic division to perform the division. - x4−2x3−13x2−8x−10x−5\frac { x ^ { 4 } - 2 x ^ { 3 } - 13 x ^ { 2 } - 8 x - 10 } { x - 5 }x−5x4−2x3−13x2−8x−10​

Provide an appropriate response. -Explain the behavior of the graph of f(x)f ( x )f(x) as it approaches its vertical asymptote. f(x)=−1(x−6)2f ( x ) = \frac { - 1 } { ( x - 6 ) ^ { 2 } }f(x)=(x−6)2−1​

Find a polynomial of least degree with only real coefficients and having the given zeros. - −3,3- \sqrt { 3 } , \sqrt { 3 }−3​,3​ , and −4i- 4 \mathrm { i }−4i

If m varies directly as x and y , and m=24 when x=6 and y=9 , find m when x=15 and y=8 .

If an object is propelled upward from a height of 144 feet at an initial velocity of 128 feet per second, then its height after t seconds is given by the equation h(t)=−16t2+128t+144h ( t ) = - 16 t ^ { 2 } + 128 t + 144h(t)=−16t2+128t+144 After how many seconds does the object Hit the ground?

Sketch the graph of the rational function. - f(x)=(x−3)(x−1)(x−2)2f ( x ) = \frac { ( x - 3 ) ( x - 1 ) } { ( x - 2 ) ^ { 2 } }f(x)=(x−2)2(x−3)(x−1)​

Factor f(x) into linear factors given that k is a zero of f(x). - f(x)=10x3+53x2+49x−12;k=15f ( x ) = 10 x ^ { 3 } + 53 x ^ { 2 } + 49 x - 12 ; k = \frac { 1 } { 5 }f(x)=10x3+53x2+49x−12;k=51​

Translate the given formula to an English phrase using the word "varies". - f−stop=fD\mathrm { f } - \mathrm { stop } = \frac { \mathrm { f } } { \mathrm { D } }f−stop=Df​ , where f-stop is camera setting with a lens with focal length f and diaphragm opening D

Provide an appropriate response. -For what value of ccc does the quadratic function f(x)=x2−6x+cf ( x ) = x ^ { 2 } - 6 x + cf(x)=x2−6x+c have exactly one xxx -intercept?

Find the correct end behavior diagram for the given polynomial function. - P(x)=−2x6+7x5−x2−2x+4P ( x ) = - 2 x ^ { 6 } + 7 x ^ { 5 } - x ^ { 2 } - 2 x + 4P(x)=−2x6+7x5−x2−2x+4

Solve the inequality. Write the solution set in interval notation. - 3x2+14x<243 x ^ { 2 } + 14 x < 243x2+14x<24

Give the equations of any horizontal asymptotes. - h(x)=7x2−9x−63x2−4x+7h ( x ) = \frac { 7 x ^ { 2 } - 9 x - 6 } { 3 x ^ { 2 } - 4 x + 7 }h(x)=3x2−4x+77x2−9x−6​

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - k=−2;f(x)=−8x3−9x2+x−26k = - 2 ; f ( x ) = - 8 x ^ { 3 } - 9 x ^ { 2 } + x - 26k=−2;f(x)=−8x3−9x2+x−26