Question 1

Find all the zeros of the function and write the polynomial as a product of linear factors. $x ^ { 4 } + 32 x ^ { 2 } + 256$

Accepted Answer

A)  $4 i , 4 i ; ( x + 4 i ) ( x + 4 i ) ( x + 4 i ) ( x + 4 i )$ 
B)  $\pm 4 , \pm 4 i ; ( x + 4 ) ( x - 4 ) ( x + 4 i ) ( x - 4 i )$ 
C)  $\pm 4 i , \pm 4 ; ( x + 4 i ) ( x - 4 i ) ( x + 4 ) ( x - 4 )$ 
D)  $- 4 i , - 4 i ; ( x - 4 i ) ( x - 4 i ) ( x - 4 i ) ( x - 4 i )$ 
E)  $\pm 4 i , \pm 4 i ; ( x + 4 i ) ( x - 4 i ) ( x + 4 i ) ( x - 4 i )$ 
A)  $4 i , 4 i ; ( x + 4 i ) ( x + 4 i ) ( x + 4 i ) ( x + 4 i )$ 
B)  $\pm 4 , \pm 4 i ; ( x + 4 ) ( x - 4 ) ( x + 4 i ) ( x - 4 i )$ 
C)  $\pm 4 i , \pm 4 ; ( x + 4 i ) ( x - 4 i ) ( x + 4 ) ( x - 4 )$ 
D)  $- 4 i , - 4 i ; ( x - 4 i ) ( x - 4 i ) ( x - 4 i ) ( x - 4 i )$ 
E)  $\pm 4 i , \pm 4 i ; ( x + 4 i ) ( x - 4 i ) ( x + 4 i ) ( x - 4 i )$

Question 2

Select the correct graph of the function given by $f ( x ) = x ^ { 4 }$ . Explain how the graph of function g differs (if it does) from the graph of each function $f$. $g ( x ) = f ( x ) + 8$

Accepted Answer

A)

Horizontal shift of eight units 
B) 
 
Vertically downward shift of eight units 
C) 
 
Horizontal shift of eight units to the 
D) 
 
Vertical shift of eight units 
E) 
 
 Horizontal shift of eight units to the left right 
A)

Horizontal shift of eight units 
B) 
 
Vertically downward shift of eight units 
C) 
 
Horizontal shift of eight units to the 
D) 
 
Vertical shift of eight units 
E) 
 
 Horizontal shift of eight units to the left right

Question 3

Find all the rational zeros of the function 
$f ( x ) = 2 x ^ { 5 } + 3 x ^ { 4 } - 9 x ^ { 3 } - 3 x ^ { 2 } - 11 x - 6$

Accepted Answer

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

Question 4

Use long division to divide. $\left( x ^ { 3 } - 4 x ^ { 2 } + 36 x - 144 \right) \div ( x - 4 )$

Accepted Answer

A)  $x ^ { 2 } - 8 x + 38 - \frac { 122 } { x - 4 }$ 
B)  $x ^ { 2 } - 8 x + 68 + \frac { 160 } { x - 4 }$ 
C)  $x ^ { 2 } - 8 x + 38$ 
D)  $x ^ { 2 } + 24$ 
E)  $x ^ { 2 } + 36$ 
A)  $x ^ { 2 } - 8 x + 38 - \frac { 122 } { x - 4 }$ 
B)  $x ^ { 2 } - 8 x + 68 + \frac { 160 } { x - 4 }$ 
C)  $x ^ { 2 } - 8 x + 38$ 
D)  $x ^ { 2 } + 24$ 
E)  $x ^ { 2 } + 36$

Question 5

Determine the domain of 
$f ( x ) = \frac { x ^ { 2 } + 9 x + 20 } { x ^ { 3 } + 5 x ^ { 2 } - x - 5 }$

Accepted Answer

A)  all real numbers except $x = - 1 , x = 1 , x = - 5$, and $x = - 4$ 
B)  all real numbers except $x = - 1 , x = 1$, and $x = - 5$ 
C)  all real numbers except $x = - 5$ and $x = - 4$ 
D)  all real numbers except $x = 5$ 
E)  all real numbers 
A)  all real numbers except $x = - 1 , x = 1 , x = - 5$, and $x = - 4$ 
B)  all real numbers except $x = - 1 , x = 1$, and $x = - 5$ 
C)  all real numbers except $x = - 5$ and $x = - 4$ 
D)  all real numbers except $x = 5$ 
E)  all real numbers

Question 6

Solve the inequality and graph the solution on the real number line. $$x ^ { 2 } - 6 x - 16 > 0$$

Accepted Answer

A) $( - \infty , - 2 ) \cup ( 8 , \infty )$
  
B)  $( - \infty , - 2 ) \cup ( - 8 , \infty )$
  
C)  $( - \infty , - 2 ) \cup ( - 8 , - \infty )$
  
D)  $( \infty , - 2 ) \cup ( 8 , - \infty )$
  
E)  $( - \infty , 2 ) \cup ( 8 , \infty )$
  
A) $( - \infty , - 2 ) \cup ( 8 , \infty )$
  
B)  $( - \infty , - 2 ) \cup ( - 8 , \infty )$
  
C)  $( - \infty , - 2 ) \cup ( - 8 , - \infty )$
  
D)  $( \infty , - 2 ) \cup ( 8 , - \infty )$
  
E)  $( - \infty , 2 ) \cup ( 8 , \infty )$

Question 7

Find domain of the following function. $$g ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } - 4 x + 3 }$$

Accepted Answer

A)  all real numbers $x$ except $x = - 9$ and $x = - 1$ 
B)  all real numbers $x$ except $x = 4$ and $x = 9$ 
C)  all real numbers $x$ except $x = - 4$ and $x = 3$ 
D)  all real numbers $x$ except $x = - 3$ and $x = 1$ 
E)  all real numbers $x$ except $x = 3$ and $x = 1$ 
A)  all real numbers $x$ except $x = - 9$ and $x = - 1$ 
B)  all real numbers $x$ except $x = 4$ and $x = 9$ 
C)  all real numbers $x$ except $x = - 4$ and $x = 3$ 
D)  all real numbers $x$ except $x = - 3$ and $x = 1$ 
E)  all real numbers $x$ except $x = 3$ and $x = 1$

Question 8

Simplify the complex number and write it in standard form. $( - i ) ^ { 6 }$

Accepted Answer

A)  i 
B)  $- 1$ 
C)  $- i$ 
D)  1 
E)  6 
A)  i 
B)  $- 1$ 
C)  $- i$ 
D)  1 
E)  6

Question 9

The cost C (in millions of dollars) removing p% the industrial and municipal pollu- tants discharged into a river is given by $C = \frac { 210 p } { 100 - p } , 0 \leq p \leq 100$ 
Select the correct graph of the cost function.

Accepted Answer

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

Question 10

Find all the rational zeros of the function. $x ^ { 3 } - 18 x ^ { 2 } + 108 x - 216$

Accepted Answer

A)  0,6 
B)  $0 , - 1$ 
C)  6 
D)  $- 6$ 
E)  $\pm 6$ 
A)  0,6 
B)  $0 , - 1$ 
C)  6 
D)  $- 6$ 
E)  $\pm 6$

Question 11

Determine the domain of $f ( x ) = \frac { x ^ { 2 } + 8 x + 15 } { x ^ { 3 } + 5 x ^ { 2 } - x - 5 }$

Accepted Answer

A)  all real numbers except $x = - 5$ and $x = - 3$ 
B)  all real numbers except $x = - 1 , x = 1 , x = - 5$, and $x = - 3$ 
C)  all real numbers except $x = 5$ 
D)  all real numbers except $x = - 1 , x = 1$, and $x = - 5$ 
E)  all real numbers 
A)  all real numbers except $x = - 5$ and $x = - 3$ 
B)  all real numbers except $x = - 1 , x = 1 , x = - 5$, and $x = - 3$ 
C)  all real numbers except $x = 5$ 
D)  all real numbers except $x = - 1 , x = 1$, and $x = - 5$ 
E)  all real numbers

Question 12

Describe the right-hand and the left-hand behavior of the graph of $n ( x ) = - \frac { 1 } { 3 } \left( x ^ { 3 } - 10 x ^ { 2 } + 6 x + 1 \right)$

Accepted Answer

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

Question 13

Find domain of the following function. $$g ( x ) = \frac { x ^ { 2 } - 16 } { x ^ { 2 } - 5 x + 4 }$$

Accepted Answer

A)  all real numbers $x$ except $x = - 16$ and $x = - 1$ 
B)  all real numbers $x$ except $x = - 5$ and $x = 4$ 
C)  all real numbers $x$ except $x = 5$ and $x = 16$ 
D)  all real numbers $x$ except $x = 4$ and $x = 1$ 
E)  all real numbers $x$ except $x = - 4$ and $x = 1$ 
A)  all real numbers $x$ except $x = - 16$ and $x = - 1$ 
B)  all real numbers $x$ except $x = - 5$ and $x = 4$ 
C)  all real numbers $x$ except $x = 5$ and $x = 16$ 
D)  all real numbers $x$ except $x = 4$ and $x = 1$ 
E)  all real numbers $x$ except $x = - 4$ and $x = 1$

Question 14

Write the complex conjugate of the complex number. Then multiply the number by its complex conjugate. $- 13 + \sqrt { 12 } i$

Accepted Answer

A)  $13 + \sqrt { 12 } i , 181$ 
B)  $- 13 + \sqrt { 12 } i , 181$ 
C)  $- 12 - \sqrt { 13 } i , 181$ 
D)  $- 13 - \sqrt { 12 } i , 181$ 
E)  $13 - \sqrt { 12 } i , 181$ 
A)  $13 + \sqrt { 12 } i , 181$ 
B)  $- 13 + \sqrt { 12 } i , 181$ 
C)  $- 12 - \sqrt { 13 } i , 181$ 
D)  $- 13 - \sqrt { 12 } i , 181$ 
E)  $13 - \sqrt { 12 } i , 181$

Question 15

Use the position equation $s = - 15 t ^ { 2 } + v _ { 0 } t + s _ { 0 }$ , where $S$ represents the height of an object (in feet), $v _ { 0 }$ represents the initial velocity of the object (in feet per second), $s _ { 0 }$ represents the Initial height of the object (in feet), and $t$ represents the time (in seconds).
A projectile is fired straight upward from ground level $\left( s _ { 0 } = 0 \right)$ with an initial velocity of $165$ feet Per second. At what instant will it be back at ground level?

Accepted Answer

A)  $t = 10 \mathrm { Sec }$ 
B)  $t = 12 \mathrm { Sec }$ 
C)  $t = 13 \mathrm { Sec }$ 
D)  $t = 9 \mathrm { Sec }$ 
E)  $t = 11 \mathrm { Sec }$ 
A)  $t = 10 \mathrm { Sec }$ 
B)  $t = 12 \mathrm { Sec }$ 
C)  $t = 13 \mathrm { Sec }$ 
D)  $t = 9 \mathrm { Sec }$ 
E)  $t = 11 \mathrm { Sec }$

Question 16

Find the domain of $x$ in the expression. Use a graphing utility to verify your result. 
$\sqrt { 25 - x ^ { 2 } }$

Accepted Answer

A)  $( - 25,25 )$ 
B)  $[ - 25,25 ]$ 
C)  $( - 5,5 )$ 
D)  $[ - 5,25 )$ 
E)  $[ - 5,5 ]$ 
A)  $( - 25,25 )$ 
B)  $[ - 25,25 ]$ 
C)  $( - 5,5 )$ 
D)  $[ - 5,25 )$ 
E)  $[ - 5,5 ]$

Question 17

Write the standard form of the equation of the parabola that has a vertex at $( - 8 , - 3 )$ and passes through the point $( - 6,2 )$

Accepted Answer

A)  $f ( x ) = \frac { 5 } { 64 } ( x - 8 ) ^ { 2 } - 3$ 
B) $f ( x ) = - \frac { 3 } { 64 } ( x + 3 ) ^ { 2 } + 6$ 
C)  $f ( x ) = \frac { 5 } { 4 } ( x + 8 ) ^ { 2 } - 3$ 
D)  $f ( x ) = \frac { 1 } { 2 } ( x + 8 ) ^ { 2 } - 6$ 
E)  $f ( x ) = \frac { 1 } { 2 } ( x + 3 ) ^ { 2 } + 2$ 
A)  $f ( x ) = \frac { 5 } { 64 } ( x - 8 ) ^ { 2 } - 3$ 
B) $f ( x ) = - \frac { 3 } { 64 } ( x + 3 ) ^ { 2 } + 6$ 
C)  $f ( x ) = \frac { 5 } { 4 } ( x + 8 ) ^ { 2 } - 3$ 
D)  $f ( x ) = \frac { 1 } { 2 } ( x + 8 ) ^ { 2 } - 6$ 
E)  $f ( x ) = \frac { 1 } { 2 } ( x + 3 ) ^ { 2 } + 2$

Question 18

Write $f ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 4 x - 16$ as a product of linear factors.

Accepted Answer

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

Question 19

Use Descartes's Rule of Signs to determine the possible numbers of positive and neg- ative zeros of the function. $6 x ^ { 5 } - 12 x$

Accepted Answer

A)  One negative zero 
B)  One negative zero or three positive zeros 
C)  Two negative zeros or no positive zero 
D)  One positive zero, one negative zero 
E)  One negative zero, four negative zeros 
A)  One negative zero 
B)  One negative zero or three positive zeros 
C)  Two negative zeros or no positive zero 
D)  One positive zero, one negative zero 
E)  One negative zero, four negative zeros

Question 20

Determine the equations of the vertical and horizontal asymptotes of the graph of the function $$f ( x ) = \frac { 2 x ^ { 2 } } { x ^ { 2 } - 9 }$$

Accepted Answer

A)  horizontal: $y = - 3$; vertical: $x = 2$ 
B)  horizontal: $x = 3$ and $x = - 3$; vertical: $y = - 2$ 
C)  horizontal: $y = 2$; vertical: $x = 3$ and $x = - 3$ 
D)  horizontal: $x = - 2$; vertical: $y = 3$ and $y = - 3$ 
E)  horizontal: $y = 2$; vertical: $x = 3$ 
A)  horizontal: $y = - 3$; vertical: $x = 2$ 
B)  horizontal: $x = 3$ and $x = - 3$; vertical: $y = - 2$ 
C)  horizontal: $y = 2$; vertical: $x = 3$ and $x = - 3$ 
D)  horizontal: $x = - 2$; vertical: $y = 3$ and $y = - 3$ 
E)  horizontal: $y = 2$; vertical: $x = 3$

Find all the zeros of the function and write the polynomial as a product of linear factors. $x ^ { 4 } + 32 x ^ { 2 } + 256$

Select the correct graph of the function given by $f ( x ) = x ^ { 4 }$ . Explain how the graph of function g differs (if it does) from the graph of each function $f$ . $g ( x ) = f ( x ) + 8$

Find all the rational zeros of the function $f ( x ) = 2 x ^ { 5 } + 3 x ^ { 4 } - 9 x ^ { 3 } - 3 x ^ { 2 } - 11 x - 6$

Use long division to divide. $\left( x ^ { 3 } - 4 x ^ { 2 } + 36 x - 144 \right) \div ( x - 4 )$

Determine the domain of $f ( x ) = \frac { x ^ { 2 } + 9 x + 20 } { x ^ { 3 } + 5 x ^ { 2 } - x - 5 }$

Solve the inequality and graph the solution on the real number line. $x ^ { 2 } - 6 x - 16 > 0$

Find domain of the following function. $g ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } - 4 x + 3 }$

Simplify the complex number and write it in standard form. $( - i ) ^ { 6 }$

The cost C (in millions of dollars) removing p% the industrial and municipal pollu- tants discharged into a river is given by $C = \frac { 210 p } { 100 - p } , 0 \leq p \leq 100$ Select the correct graph of the cost function.

Find all the rational zeros of the function. $x ^ { 3 } - 18 x ^ { 2 } + 108 x - 216$

Determine the domain of $f ( x ) = \frac { x ^ { 2 } + 8 x + 15 } { x ^ { 3 } + 5 x ^ { 2 } - x - 5 }$

Describe the right-hand and the left-hand behavior of the graph of $n ( x ) = - \frac { 1 } { 3 } \left( x ^ { 3 } - 10 x ^ { 2 } + 6 x + 1 \right)$

Find domain of the following function. $g ( x ) = \frac { x ^ { 2 } - 16 } { x ^ { 2 } - 5 x + 4 }$

Write the complex conjugate of the complex number. Then multiply the number by its complex conjugate. $- 13 + \sqrt { 12 } i$

Find the domain of $x$ in the expression. Use a graphing utility to verify your result. $\sqrt { 25 - x ^ { 2 } }$

Write the standard form of the equation of the parabola that has a vertex at $( - 8 , - 3 )$ and passes through the point $( - 6,2 )$

Write $f ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 4 x - 16$ as a product of linear factors.

Use Descartes's Rule of Signs to determine the possible numbers of positive and neg- ative zeros of the function. $6 x ^ { 5 } - 12 x$

Determine the equations of the vertical and horizontal asymptotes of the graph of the function $f ( x ) = \frac { 2 x ^ { 2 } } { x ^ { 2 } - 9 }$

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Topics in Analytic Geometry

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Exam 2: Polynomial and Rational Functions

Find all the zeros of the function and write the polynomial as a product of linear factors. x4+32x2+256x ^ { 4 } + 32 x ^ { 2 } + 256x4+32x2+256

Select the correct graph of the function given by f(x)=x4f ( x ) = x ^ { 4 }f(x)=x4 . Explain how the graph of function g differs (if it does) from the graph of each function fff . g(x)=f(x)+8g ( x ) = f ( x ) + 8g(x)=f(x)+8

Find all the rational zeros of the function f(x)=2x5+3x4−9x3−3x2−11x−6f ( x ) = 2 x ^ { 5 } + 3 x ^ { 4 } - 9 x ^ { 3 } - 3 x ^ { 2 } - 11 x - 6f(x)=2x5+3x4−9x3−3x2−11x−6

Use long division to divide. (x3−4x2+36x−144)÷(x−4)\left( x ^ { 3 } - 4 x ^ { 2 } + 36 x - 144 \right) \div ( x - 4 )(x3−4x2+36x−144)÷(x−4)

Determine the domain of f(x)=x2+9x+20x3+5x2−x−5f ( x ) = \frac { x ^ { 2 } + 9 x + 20 } { x ^ { 3 } + 5 x ^ { 2 } - x - 5 }f(x)=x3+5x2−x−5x2+9x+20​

Solve the inequality and graph the solution on the real number line. x2−6x−16>0x ^ { 2 } - 6 x - 16 > 0x2−6x−16>0

Find domain of the following function. g(x)=x2−9x2−4x+3g ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } - 4 x + 3 }g(x)=x2−4x+3x2−9​

Simplify the complex number and write it in standard form. (−i)6( - i ) ^ { 6 }(−i)6

The cost C (in millions of dollars) removing p% the industrial and municipal pollu- tants discharged into a river is given by C=210p100−p,0≤p≤100C = \frac { 210 p } { 100 - p } , 0 \leq p \leq 100C=100−p210p​,0≤p≤100 Select the correct graph of the cost function.

Find all the rational zeros of the function. x3−18x2+108x−216x ^ { 3 } - 18 x ^ { 2 } + 108 x - 216x3−18x2+108x−216

Determine the domain of f(x)=x2+8x+15x3+5x2−x−5f ( x ) = \frac { x ^ { 2 } + 8 x + 15 } { x ^ { 3 } + 5 x ^ { 2 } - x - 5 }f(x)=x3+5x2−x−5x2+8x+15​

Describe the right-hand and the left-hand behavior of the graph of n(x)=−13(x3−10x2+6x+1)n ( x ) = - \frac { 1 } { 3 } \left( x ^ { 3 } - 10 x ^ { 2 } + 6 x + 1 \right)n(x)=−31​(x3−10x2+6x+1)

Find domain of the following function. g(x)=x2−16x2−5x+4g ( x ) = \frac { x ^ { 2 } - 16 } { x ^ { 2 } - 5 x + 4 }g(x)=x2−5x+4x2−16​

Write the complex conjugate of the complex number. Then multiply the number by its complex conjugate. −13+12i- 13 + \sqrt { 12 } i−13+12​i

Find the domain of xxx in the expression. Use a graphing utility to verify your result. 25−x2\sqrt { 25 - x ^ { 2 } }25−x2​

Write the standard form of the equation of the parabola that has a vertex at (−8,−3)( - 8 , - 3 )(−8,−3) and passes through the point (−6,2)( - 6,2 )(−6,2)

Write f(x)=x3−4x2+4x−16f ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 4 x - 16f(x)=x3−4x2+4x−16 as a product of linear factors.

Use Descartes's Rule of Signs to determine the possible numbers of positive and neg- ative zeros of the function. 6x5−12x6 x ^ { 5 } - 12 x6x5−12x

Determine the equations of the vertical and horizontal asymptotes of the graph of the function f(x)=2x2x2−9f ( x ) = \frac { 2 x ^ { 2 } } { x ^ { 2 } - 9 }f(x)=x2−92x2​

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Topics in Analytic Geometry

Filters

Find all the zeros of the function and write the polynomial as a product of linear factors. $x ^ { 4 } + 32 x ^ { 2 } + 256$

Select the correct graph of the function given by $f ( x ) = x ^ { 4 }$ . Explain how the graph of function g differs (if it does) from the graph of each function $f$ . $g ( x ) = f ( x ) + 8$

Find all the rational zeros of the function $f ( x ) = 2 x ^ { 5 } + 3 x ^ { 4 } - 9 x ^ { 3 } - 3 x ^ { 2 } - 11 x - 6$

Use long division to divide. $\left( x ^ { 3 } - 4 x ^ { 2 } + 36 x - 144 \right) \div ( x - 4 )$

Determine the domain of $f ( x ) = \frac { x ^ { 2 } + 9 x + 20 } { x ^ { 3 } + 5 x ^ { 2 } - x - 5 }$

Solve the inequality and graph the solution on the real number line. $x ^ { 2 } - 6 x - 16 > 0$

Find domain of the following function. $g ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } - 4 x + 3 }$

Simplify the complex number and write it in standard form. $( - i ) ^ { 6 }$

The cost C (in millions of dollars) removing p% the industrial and municipal pollu- tants discharged into a river is given by $C = \frac { 210 p } { 100 - p } , 0 \leq p \leq 100$ Select the correct graph of the cost function.

Find all the rational zeros of the function. $x ^ { 3 } - 18 x ^ { 2 } + 108 x - 216$

Determine the domain of $f ( x ) = \frac { x ^ { 2 } + 8 x + 15 } { x ^ { 3 } + 5 x ^ { 2 } - x - 5 }$

Describe the right-hand and the left-hand behavior of the graph of $n ( x ) = - \frac { 1 } { 3 } \left( x ^ { 3 } - 10 x ^ { 2 } + 6 x + 1 \right)$

Find domain of the following function. $g ( x ) = \frac { x ^ { 2 } - 16 } { x ^ { 2 } - 5 x + 4 }$

Write the complex conjugate of the complex number. Then multiply the number by its complex conjugate. $- 13 + \sqrt { 12 } i$

Find the domain of $x$ in the expression. Use a graphing utility to verify your result. $\sqrt { 25 - x ^ { 2 } }$

Write the standard form of the equation of the parabola that has a vertex at $( - 8 , - 3 )$ and passes through the point $( - 6,2 )$

Write $f ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 4 x - 16$ as a product of linear factors.

Use Descartes's Rule of Signs to determine the possible numbers of positive and neg- ative zeros of the function. $6 x ^ { 5 } - 12 x$

Determine the equations of the vertical and horizontal asymptotes of the graph of the function $f ( x ) = \frac { 2 x ^ { 2 } } { x ^ { 2 } - 9 }$