Question 1

Use synthetic division to divide. $\left( - 12 + 2 x ^ { 3 } + 22 x - 12 x ^ { 2 } \right) \div ( x - 3 )$

Accepted Answer

A)   $2 x ^ { 2 } - 5 x + 3$ 
B)   $2 x ^ { 2 } - 10 x - 8$ 
C)   $2 x ^ { 2 } - x + 12$ 
D)   $2 x ^ { 2 } - 6 x + 4$ 
E)   $2 x ^ { 2 } + 6 x - 2$ 
A)   $2 x ^ { 2 } - 5 x + 3$ 
B)   $2 x ^ { 2 } - 10 x - 8$ 
C)   $2 x ^ { 2 } - x + 12$ 
D)   $2 x ^ { 2 } - 6 x + 4$ 
E)   $2 x ^ { 2 } + 6 x - 2$

Question 2

Determine the zeros (if any) of the rational function $g ( x ) = 5 + \frac { 6 } { x ^ { 2 } + 5 }$ .

Accepted Answer

A) no zeros 
B)  $x = - \sqrt { 5 } , x = \sqrt { 5 }$ 
C)  x = -5, x = 5 
D)   $x = - \frac { 6 } { 5 } , x = \frac { 6 } { 5 }$ 
E)  x = -6 
A) no zeros 
B)  $x = - \sqrt { 5 } , x = \sqrt { 5 }$ 
C)  x = -5, x = 5 
D)   $x = - \frac { 6 } { 5 } , x = \frac { 6 } { 5 }$ 
E)  x = -6

Question 3

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

Accepted Answer

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)  $f ( x ) = x ^ { 5 } - 20 x ^ { 3 } - 64 x$ 
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 4

Let $P ( x ) = 7 x ^ { 3 } + 4 x ^ { 2 } - 9 x + 10$ .  
Use synthetic division to find the value P (-6).

Accepted Answer

A) -2,608 
B) -1,303 
C) -1,305 
D) -1,304 
E) none of these 
A) -2,608 
B) -1,303 
C) -1,305 
D) -1,304 
E) none of these

Question 5

Find domain of the following function. 
 $g ( x ) = \frac { 1 } { x + 7 }$

Accepted Answer

A) all real numbers x except x = -7 
B) all real numbers x except x = 1 
C) all real numbers x except x = 49 
D) all real numbers x except x = 7 
E) all real numbers x except x = -1 
A) all real numbers x except x = -7 
B) all real numbers x except x = 1 
C) all real numbers x except x = 49 
D) all real numbers x except x = 7 
E) all real numbers x except x = -1

Question 6

Determine the equations of the vertical and horizontal asymptotes of the graph of the function $f ( x ) = \frac { 5 x ^ { 2 } } { x ^ { 2 } - 4 }$ .

Accepted Answer

A) horizontal: y = -2; vertical: x = 5 
B) horizontal: x = 2 and x = -2; vertical: y = -5 
C) horizontal: y = 5; vertical: x = 2 and x = -2 
D) horizontal: x = -5; vertical: y = 2 and y = -2 
E) horizontal: y = 5; vertical: x = 2 
A) horizontal: y = -2; vertical: x = 5 
B) horizontal: x = 2 and x = -2; vertical: y = -5 
C) horizontal: y = 5; vertical: x = 2 and x = -2 
D) horizontal: x = -5; vertical: y = 2 and y = -2 
E) horizontal: y = 5; vertical: x = 2

Question 7

Solve the inequality and graph the solution on the real number line. 
 $x ^ { 3 } - 3 x ^ { 2 } - x > - 3$

Accepted Answer

A)  $( - 1,1 ) \cup ( 3 , \infty )$   
B)  $( - 1,1 ) \cup ( - 3 , \infty )$   
C)  $( - 1,1 ) \cup ( 3 , \infty )$   
D)  $( - 1,1 ) \cup ( - 3 , - \infty )$   
E)  $( - 1,1 ) \cup ( - 3 , \infty )$   
A)  $( - 1,1 ) \cup ( 3 , \infty )$   
B)  $( - 1,1 ) \cup ( - 3 , \infty )$   
C)  $( - 1,1 ) \cup ( 3 , \infty )$   
D)  $( - 1,1 ) \cup ( - 3 , - \infty )$   
E)  $( - 1,1 ) \cup ( - 3 , \infty )$

Question 8

Simplify the expression. ​
I -14
​

Accepted Answer

A) i 
B) -3i 
C) -i 
D) -1 
E) 1 
A) i 
B) -3i 
C) -i 
D) -1 
E) 1

Question 9

Find the domain of x in the expression. 
 $\sqrt { \frac { x } { x ^ { 2 } - 36 } }$

Accepted Answer

A)  $( - 36,0 ] \cup ( 36 , \infty )$ 
B)  $( - 36,0 ] \cap ( 36 , \infty )$ 
C)  $( - 36,0 ] \cap ( 6 , \infty )$ 
D)  $( - 6,0 ] \cup ( 6 , \infty )$ 
E)  $( - 36,0 ] \cap ( - 6 , \infty )$ 
A)  $( - 36,0 ] \cup ( 36 , \infty )$ 
B)  $( - 36,0 ] \cap ( 36 , \infty )$ 
C)  $( - 36,0 ] \cap ( 6 , \infty )$ 
D)  $( - 6,0 ] \cup ( 6 , \infty )$ 
E)  $( - 36,0 ] \cap ( - 6 , \infty )$

Question 10

Write the complex number in standard form.
 $\sqrt { - 36 }$

Accepted Answer

A) 6i 
B) -6i 
C) 36i 
D) 7i 
E) -36i 
A) 6i 
B) -6i 
C) 36i 
D) 7i 
E) -36i

Question 11

Find all the real zeros of $f ( x ) = 2 x ^ { 3 } - 6 x ^ { 2 } + 2 x - 6$ .

Accepted Answer

A)  x = 3, $- \frac { 1 } { 3 }$ 
B)  x = 2, 1, -6 
C)  x = ± 1, 3 
D)  x = 3 
E)  x = $\frac { 1 } { 2 }$ , $- \frac { 1 } { 6 }$ 
A)  x = 3, $- \frac { 1 } { 3 }$ 
B)  x = 2, 1, -6 
C)  x = ± 1, 3 
D)  x = 3 
E)  x = $\frac { 1 } { 2 }$ , $- \frac { 1 } { 6 }$

Question 12

A rectangular parking lot with a perimeter of 442 feet is to have an area of at least 8050 square feet.Within what bounds must the length of the rectangle lie?

Accepted Answer

A)  $8050 \mathrm { ft } \leq L \leq 442 \mathrm { ft }$ 
B)  $177 \mathrm { ft } \leq L \leq 48 \mathrm { ft }$ 
C)  $49 \mathrm { ft } \leq L \leq 178 \mathrm { ft }$ 
D)  $8050 \mathrm { ft } \leq L \leq 47 \mathrm { ft }$ 
E)  $46 \mathrm { ft } \leq L \leq 175 \mathrm { ft }$ 
A)  $8050 \mathrm { ft } \leq L \leq 442 \mathrm { ft }$ 
B)  $177 \mathrm { ft } \leq L \leq 48 \mathrm { ft }$ 
C)  $49 \mathrm { ft } \leq L \leq 178 \mathrm { ft }$ 
D)  $8050 \mathrm { ft } \leq L \leq 47 \mathrm { ft }$ 
E)  $46 \mathrm { ft } \leq L \leq 175 \mathrm { ft }$

Question 13

The game commission introduces 100 deer into newly acquired state game lands.The population N of the herd is modeled by 
 $N = \frac { 24 ( 5 + 3 t ) } { 1 + 0.04 t } , t \geq 0$  
Where t is the time in years.Find the populations when t = 40.
(Round your answer to the nearest whole number.)

Accepted Answer

A) 1,154 deer 
B) 1,306 deer 
C) 1,275 deer 
D) 1,240 deer 
E) 1,200 deer 
A) 1,154 deer 
B) 1,306 deer 
C) 1,275 deer 
D) 1,240 deer 
E) 1,200 deer

Question 14

Write the standard form of the equation of the parabola that has a vertex at $\left( - \frac { 2 } { 3 } , \frac { 1 } { 9 } \right)$ and passes through the point $( 2,3 )$ .

Accepted Answer

A)  $f ( x ) = \frac { 13 } { 32 } \left( x - \frac { 3 } { 2 } \right) ^ { 2 } + \frac { 1 } { 9 }$ 
B)  $f ( x ) = \frac { 13 } { 32 } \left( x + \frac { 2 } { 3 } \right) ^ { 2 } + \frac { 1 } { 9 }$ 
C)  $f ( x ) = \frac { 13 } { 4 } \left( x - \frac { 2 } { 3 } \right) ^ { 2 } - \frac { 1 } { 9 }$ 
D)  $f ( x ) = \frac { 13 } { 8 } \left( x - \frac { 3 } { 2 } \right) ^ { 2 } - \frac { 1 } { 9 }$ 
E)  $f ( x ) = \frac { 13 } { 4 } \left( x + \frac { 2 } { 3 } \right) ^ { 2 } + \frac { 1 } { 9 }$ 
A)  $f ( x ) = \frac { 13 } { 32 } \left( x - \frac { 3 } { 2 } \right) ^ { 2 } + \frac { 1 } { 9 }$ 
B)  $f ( x ) = \frac { 13 } { 32 } \left( x + \frac { 2 } { 3 } \right) ^ { 2 } + \frac { 1 } { 9 }$ 
C)  $f ( x ) = \frac { 13 } { 4 } \left( x - \frac { 2 } { 3 } \right) ^ { 2 } - \frac { 1 } { 9 }$ 
D)  $f ( x ) = \frac { 13 } { 8 } \left( x - \frac { 3 } { 2 } \right) ^ { 2 } - \frac { 1 } { 9 }$ 
E)  $f ( x ) = \frac { 13 } { 4 } \left( x + \frac { 2 } { 3 } \right) ^ { 2 } + \frac { 1 } { 9 }$

Question 15

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

Accepted Answer

A) even 
B) odd 
C) neither 
A) even 
B) odd 
C) neither

Question 16

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

Accepted Answer

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: $0,4 \sqrt { 2 }$   
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 17

Write the quotient in standard form. 
 $\frac { 2 } { i }$

Accepted Answer

A)   $- \frac { i } { 2 }$ 
B)  $- \frac { 2 } { i }$ 
C)  -2i 
D)   $\frac { i } { 2 }$ 
E)  2i 
A)   $- \frac { i } { 2 }$ 
B)  $- \frac { 2 } { i }$ 
C)  -2i 
D)   $\frac { i } { 2 }$ 
E)  2i

Question 18

Write the complex number in standard form. 
$\sqrt { - 20 } \times \sqrt { - 18 }$

Accepted Answer

A)  $6 \sqrt { 10 }$ 
B)  $- \sqrt { 20 }$ 
C)  - $6 \sqrt { 10 }$ 
D)  $\sqrt { 18 }$ 
E)  $\sqrt { 20 }$ 
A)  $6 \sqrt { 10 }$ 
B)  $- \sqrt { 20 }$ 
C)  - $6 \sqrt { 10 }$ 
D)  $\sqrt { 18 }$ 
E)  $\sqrt { 20 }$

Question 19

Find the domain of the function $f ( x ) = \frac { 6 x ^ { 2 } } { x ^ { 2 } - 25 }$ .

Accepted Answer

A) Domain: all real numbers x except x =  5 
B) Domain: all real numbers x except x =  ±25 
C) Domain: all real numbers x except x = ±6 
D) Domain: all real numbers x except x =  -5 
E) Domain: all real numbers x except x =  ±5 
A) Domain: all real numbers x except x =  5 
B) Domain: all real numbers x except x =  ±25 
C) Domain: all real numbers x except x = ±6 
D) Domain: all real numbers x except x =  -5 
E) Domain: all real numbers x except x =  ±5

Question 20

Use synthetic division to divide. 
 $\frac { x ^ { 3 } - 125 } { x - 5 }$

Accepted Answer

A)   $x ^ { 2 } + 5 x + 25 , x \neq 5$ 
B)  $x ^ { 2 } + 5 x - 25 , x \neq - 5$ 
C)  $x ^ { 2 } - 5 x + 25 , x \neq - 5$ 
D)  $- x ^ { 2 } + 5 x + 25 , x \neq - 5$ 
E)  $x ^ { 2 } - 5 x - 25 , x \neq - 5$ 
A)   $x ^ { 2 } + 5 x + 25 , x \neq 5$ 
B)  $x ^ { 2 } + 5 x - 25 , x \neq - 5$ 
C)  $x ^ { 2 } - 5 x + 25 , x \neq - 5$ 
D)  $- x ^ { 2 } + 5 x + 25 , x \neq - 5$ 
E)  $x ^ { 2 } - 5 x - 25 , x \neq - 5$

Use synthetic division to divide. $\left( - 12 + 2 x ^ { 3 } + 22 x - 12 x ^ { 2 } \right) \div ( x - 3 )$

Determine the zeros (if any) of the rational function $g ( x ) = 5 + \frac { 6 } { x ^ { 2 } + 5 }$ .

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

Let $P ( x ) = 7 x ^ { 3 } + 4 x ^ { 2 } - 9 x + 10$ . Use synthetic division to find the value P (-6).

Find domain of the following function. $g ( x ) = \frac { 1 } { x + 7 }$

Determine the equations of the vertical and horizontal asymptotes of the graph of the function $f ( x ) = \frac { 5 x ^ { 2 } } { x ^ { 2 } - 4 }$ .

Solve the inequality and graph the solution on the real number line. $x ^ { 3 } - 3 x ^ { 2 } - x > - 3$

Simplify the expression. I ^-14

Find the domain of x in the expression. $\sqrt { \frac { x } { x ^ { 2 } - 36 } }$

Write the complex number in standard form. $\sqrt { - 36 }$

Find all the real zeros of $f ( x ) = 2 x ^ { 3 } - 6 x ^ { 2 } + 2 x - 6$ .

A rectangular parking lot with a perimeter of 442 feet is to have an area of at least 8050 square feet.Within what bounds must the length of the rectangle lie?

The game commission introduces 100 deer into newly acquired state game lands.The population N of the herd is modeled by $N = \frac { 24 ( 5 + 3 t ) } { 1 + 0.04 t } , t \geq 0$ Where t is the time in years.Find the populations when t = 40. (Round your answer to the nearest whole number.)

Write the standard form of the equation of the parabola that has a vertex at $\left( - \frac { 2 } { 3 } , \frac { 1 } { 9 } \right)$ and passes through the point $( 2,3 )$ .

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

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

Write the quotient in standard form. $\frac { 2 } { i }$

Write the complex number in standard form. $\sqrt { - 20 } \times \sqrt { - 18 }$

Find the domain of the function $f ( x ) = \frac { 6 x ^ { 2 } } { x ^ { 2 } - 25 }$ .

Use synthetic division to divide. $\frac { x ^ { 3 } - 125 } { x - 5 }$

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

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Exam 2: Polynomial and Rational Functions

Use synthetic division to divide. (−12+2x3+22x−12x2)÷(x−3)\left( - 12 + 2 x ^ { 3 } + 22 x - 12 x ^ { 2 } \right) \div ( x - 3 )(−12+2x3+22x−12x2)÷(x−3)

Determine the zeros (if any) of the rational function g(x)=5+6x2+5g ( x ) = 5 + \frac { 6 } { x ^ { 2 } + 5 }g(x)=5+x2+56​ .

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

Let P(x)=7x3+4x2−9x+10P ( x ) = 7 x ^ { 3 } + 4 x ^ { 2 } - 9 x + 10P(x)=7x3+4x2−9x+10 . Use synthetic division to find the value P (-6).

Find domain of the following function. g(x)=1x+7g ( x ) = \frac { 1 } { x + 7 }g(x)=x+71​

Determine the equations of the vertical and horizontal asymptotes of the graph of the function f(x)=5x2x2−4f ( x ) = \frac { 5 x ^ { 2 } } { x ^ { 2 } - 4 }f(x)=x2−45x2​ .

Solve the inequality and graph the solution on the real number line. x3−3x2−x>−3x ^ { 3 } - 3 x ^ { 2 } - x > - 3x3−3x2−x>−3

Simplify the expression. ​ I -14 ​

Find the domain of x in the expression. xx2−36\sqrt { \frac { x } { x ^ { 2 } - 36 } }x2−36x​​

Write the complex number in standard form. −36\sqrt { - 36 }−36​

Find all the real zeros of f(x)=2x3−6x2+2x−6f ( x ) = 2 x ^ { 3 } - 6 x ^ { 2 } + 2 x - 6f(x)=2x3−6x2+2x−6 .

A rectangular parking lot with a perimeter of 442 feet is to have an area of at least 8050 square feet.Within what bounds must the length of the rectangle lie?

Write the standard form of the equation of the parabola that has a vertex at (−23,19)\left( - \frac { 2 } { 3 } , \frac { 1 } { 9 } \right)(−32​,91​) and passes through the point (2,3)( 2,3 )(2,3) .

Well whether the function y=x5+9x3y = x ^ { 5 } + 9 x ^ { 3 }y=x5+9x3 is even or odd.If it is neither, so indicate.

Select the graph of the function and use the zero or root feature to approximate the real zeros of the function. f(x)=18x4−4x2f ( x ) = \frac { 1 } { 8 } x ^ { 4 } - 4 x ^ { 2 }f(x)=81​x4−4x2

Write the quotient in standard form. 2i\frac { 2 } { i }i2​

Write the complex number in standard form. −20×−18\sqrt { - 20 } \times \sqrt { - 18 }−20​×−18​

Find the domain of the function f(x)=6x2x2−25f ( x ) = \frac { 6 x ^ { 2 } } { x ^ { 2 } - 25 }f(x)=x2−256x2​ .

Use synthetic division to divide. x3−125x−5\frac { x ^ { 3 } - 125 } { x - 5 }x−5x3−125​

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Use synthetic division to divide. $\left( - 12 + 2 x ^ { 3 } + 22 x - 12 x ^ { 2 } \right) \div ( x - 3 )$

Determine the zeros (if any) of the rational function $g ( x ) = 5 + \frac { 6 } { x ^ { 2 } + 5 }$ .

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

Let $P ( x ) = 7 x ^ { 3 } + 4 x ^ { 2 } - 9 x + 10$ . Use synthetic division to find the value P (-6).

Find domain of the following function. $g ( x ) = \frac { 1 } { x + 7 }$

Determine the equations of the vertical and horizontal asymptotes of the graph of the function $f ( x ) = \frac { 5 x ^ { 2 } } { x ^ { 2 } - 4 }$ .

Solve the inequality and graph the solution on the real number line. $x ^ { 3 } - 3 x ^ { 2 } - x > - 3$

Simplify the expression. I ^-14

Find the domain of x in the expression. $\sqrt { \frac { x } { x ^ { 2 } - 36 } }$

Write the complex number in standard form. $\sqrt { - 36 }$

Find all the real zeros of $f ( x ) = 2 x ^ { 3 } - 6 x ^ { 2 } + 2 x - 6$ .

Write the standard form of the equation of the parabola that has a vertex at $\left( - \frac { 2 } { 3 } , \frac { 1 } { 9 } \right)$ and passes through the point $( 2,3 )$ .

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

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

Write the quotient in standard form. $\frac { 2 } { i }$

Write the complex number in standard form. $\sqrt { - 20 } \times \sqrt { - 18 }$

Find the domain of the function $f ( x ) = \frac { 6 x ^ { 2 } } { x ^ { 2 } - 25 }$ .

Use synthetic division to divide. $\frac { x ^ { 3 } - 125 } { x - 5 }$