Question 1

Determine the zeros (if any) of the rational function $f ( x ) = \frac { x ^ { 2 } - 64 } { x + 5 }$.

Accepted Answer

A)  $x = - 5$ 
B)  $x = - \frac { 8 } { 5 } , x = \frac { 8 } { 5 }$ 
C)  $x = - 64 , x = 64$ 
D)  $x = - 8 , x = 8$ 
E)  no zeros 
A)  $x = - 5$ 
B)  $x = - \frac { 8 } { 5 } , x = \frac { 8 } { 5 }$ 
C)  $x = - 64 , x = 64$ 
D)  $x = - 8 , x = 8$ 
E)  no zeros

Question 2

If $x = - 1$ is a root of $x ^ { 3 } + 2 x ^ { 2 } - x - 2 = 0$, use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Accepted Answer

A)  $( x - 2 ) ( x + 1 ) ( x - 1 ) ; x = 2 , - 1,1$ 
B)  $( x + 2 ) ( x + 1 ) ( x - 1 ) ; x = - 2 , - 1,1$ 
C)  $( x + 2 ) ( x + 1 ) ^ { 2 } ; x = - 2 , - 1$ 
D)  $( x + 2 ) ^ { 2 } ( x + 1 ) ; x = - 2 , - 1$ 
E)  $( x + 2 ) ( x - 2 ) ( x - 1 ) ; x = - 2,2,1$ 
A)  $( x - 2 ) ( x + 1 ) ( x - 1 ) ; x = 2 , - 1,1$ 
B)  $( x + 2 ) ( x + 1 ) ( x - 1 ) ; x = - 2 , - 1,1$ 
C)  $( x + 2 ) ( x + 1 ) ^ { 2 } ; x = - 2 , - 1$ 
D)  $( x + 2 ) ^ { 2 } ( x + 1 ) ; x = - 2 , - 1$ 
E)  $( x + 2 ) ( x - 2 ) ( x - 1 ) ; x = - 2,2,1$

Question 3

Write $f ( x ) = x ^ { 4 } - 12 x ^ { 3 } + 59 x ^ { 2 } - 138 x + 130$ as a product of linear factors.

Accepted Answer

A)  $( x - 3 - i ) ( x - 3 + 2 i ) ( x - 3 - 2 i ) ( x - 2 + i )$ 
B)  $( x - 3 - i ) ( x - 3 + i ) ( x - 2 - i ) ( x - 2 + i )$ 
C)  $( x - 3 - i ) ( x - 3 + i ) ( x + 3 - 2 i ) ( x - 2 + i )$ 
D)  $( x - 3 + i ) ( x - 3 - i ) ( x - 2 + 3 i ) ( x - 2 - 3 i )$ 
E)  $( x - 3 + i ) ( x - 3 - i ) ( x - 3 + 2 i ) ( x - 3 - 2 i )$ 
A)  $( x - 3 - i ) ( x - 3 + 2 i ) ( x - 3 - 2 i ) ( x - 2 + i )$ 
B)  $( x - 3 - i ) ( x - 3 + i ) ( x - 2 - i ) ( x - 2 + i )$ 
C)  $( x - 3 - i ) ( x - 3 + i ) ( x + 3 - 2 i ) ( x - 2 + i )$ 
D)  $( x - 3 + i ) ( x - 3 - i ) ( x - 2 + 3 i ) ( x - 2 - 3 i )$ 
E)  $( x - 3 + i ) ( x - 3 - i ) ( x - 3 + 2 i ) ( x - 3 - 2 i )$

Question 4

Which of the given graphs is the graph of the polynomial function below?
$$h ( x ) = x ^ { 5 } - \frac { 3 } { 2 } x ^ { 3 } - \frac { 1 } { 2 } x$$

Graph 1:

Graph 2 :

Graph 3 :
 
 Graph 4 :

Graph 5 :

Accepted Answer

A)  Graph 2 
B)  Graph 5 
C)  Graph 4 
D)  Graph 1 
E)  Graph 3 
A)  Graph 2 
B)  Graph 5 
C)  Graph 4 
D)  Graph 1 
E)  Graph 3

Question 5

If $f ( x ) = 4 x ^ { 2 } - 2 x - 7$, use synthetic division to evaluate $f \left( \frac { 7 } { 8 } \right)$.

Accepted Answer

A)  $f \left( \frac { 7 } { 8 } \right) = \frac { 21 } { 2 }$ 
B)  $f \left( \frac { 7 } { 8 } \right) = - \frac { 21 } { 2 }$ 
C)  $f \left( \frac { 7 } { 8 } \right) = - \frac { 91 } { 16 }$ 
D)  $f \left( \frac { 7 } { 8 } \right) = - \frac { 35 } { 2 }$ 
E)  $f \left( \frac { 7 } { 8 } \right) = - \frac { 77 } { 8 }$ 
A)  $f \left( \frac { 7 } { 8 } \right) = \frac { 21 } { 2 }$ 
B)  $f \left( \frac { 7 } { 8 } \right) = - \frac { 21 } { 2 }$ 
C)  $f \left( \frac { 7 } { 8 } \right) = - \frac { 91 } { 16 }$ 
D)  $f \left( \frac { 7 } { 8 } \right) = - \frac { 35 } { 2 }$ 
E)  $f \left( \frac { 7 } { 8 } \right) = - \frac { 77 } { 8 }$

Question 6

Find the quadratic function $f$ whose graph intersects the $x$-axis at $( - 7,0 )$ and $( 1,0 )$ and the $y$-axis at $( 0 , - 14 )$.

Accepted Answer

A)  $f ( x ) = - 2 x ^ { 2 } - 16 x - 2$ 
B)  $f ( x ) = 2 x ^ { 2 } + 12 x - 14$ 
C)  $f ( x ) = 2 x ^ { 2 } + 16 x - 7$ 
D)  $f ( x ) = - 2 x ^ { 2 } + 16 x - 14$ 
E)  $f ( x ) = - 2 x ^ { 2 } - 12 x - 14$ 
A)  $f ( x ) = - 2 x ^ { 2 } - 16 x - 2$ 
B)  $f ( x ) = 2 x ^ { 2 } + 12 x - 14$ 
C)  $f ( x ) = 2 x ^ { 2 } + 16 x - 7$ 
D)  $f ( x ) = - 2 x ^ { 2 } + 16 x - 14$ 
E)  $f ( x ) = - 2 x ^ { 2 } - 12 x - 14$

Question 7

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } - 80 x ^ { 2 } + 1024$ and determine the mutiplicity of each.

Accepted Answer

A)  $x = 64$, multiplicity $2 ; x = 16$, multiplicity 2 
B)  $x = 8$, multiplicity $2 ; x = 4$, multiplicity 2 
C)  $x = 64$, multiplicity $2 ; x = 4$, multiplicity 1 
D)  $x = - 8$, multiplicity $2 ; x = - 4$, multiplicity 2 
E)  $x = 8$, multiplicity $1 ; x = - 8$, multiplicity $1 ; x = 4$, multiplicity $1 ; x = - 4$, multiplicity 1 
A)  $x = 64$, multiplicity $2 ; x = 16$, multiplicity 2 
B)  $x = 8$, multiplicity $2 ; x = 4$, multiplicity 2 
C)  $x = 64$, multiplicity $2 ; x = 4$, multiplicity 1 
D)  $x = - 8$, multiplicity $2 ; x = - 4$, multiplicity 2 
E)  $x = 8$, multiplicity $1 ; x = - 8$, multiplicity $1 ; x = 4$, multiplicity $1 ; x = - 4$, multiplicity 1

Question 8

Using the factors $( - 5 x + 2 )$ and $( x - 1 )$, find the remaining factor(s) of $f ( x ) = 10 x ^ { 4 } + 31 x ^ { 3 } - 84 x ^ { 2 } + 53 x - 10$ and write the polynomial in fully factored form.

Accepted Answer

A)  $f ( x ) = ( - 5 x + 2 ) ( - 5 x + 2 ) ( 2 x - 1 ) ( x - 1 )$ 
B)  $f ( x ) = ( - 5 x + 2 ) ( - x - 5 ) ( 2 x - 1 ) ( x - 1 )$ 
C)  $f ( x ) = ( - 5 x + 2 ) ^ { 2 } ( 2 x - 1 ) ( x + 1 )$ 
D)  $f ( x ) = ( - 5 x + 2 ) ( - x + 5 ) ^ { 2 } ( x + 1 )$ 
E)  $f ( x ) = ( - 5 x + 2 ) ^ { 2 } ( x - 1 ) ^ { 2 }$ 
A)  $f ( x ) = ( - 5 x + 2 ) ( - 5 x + 2 ) ( 2 x - 1 ) ( x - 1 )$ 
B)  $f ( x ) = ( - 5 x + 2 ) ( - x - 5 ) ( 2 x - 1 ) ( x - 1 )$ 
C)  $f ( x ) = ( - 5 x + 2 ) ^ { 2 } ( 2 x - 1 ) ( x + 1 )$ 
D)  $f ( x ) = ( - 5 x + 2 ) ( - x + 5 ) ^ { 2 } ( x + 1 )$ 
E)  $f ( x ) = ( - 5 x + 2 ) ^ { 2 } ( x - 1 ) ^ { 2 }$

Question 9

Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 16 }$.

Accepted Answer

A)  horizontal: $y = 4$; vertical: $x = - 4$ 
B)  horizontal: $x = 1$; vertical: none 
C)  horizontal: $y = - 4$; vertical: $x = 1$ 
D)  horizontal: $y = 1$; vertical: none 
E)  horizontal: none; vertical: none 
A)  horizontal: $y = 4$; vertical: $x = - 4$ 
B)  horizontal: $x = 1$; vertical: none 
C)  horizontal: $y = - 4$; vertical: $x = 1$ 
D)  horizontal: $y = 1$; vertical: none 
E)  horizontal: none; vertical: none

Question 10

Write the polynomial in completely factored form. (Hint: One factor is $x ^ { 2 } + 1$.)
$f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + 14 x ^ { 2 } + 6 x + 13$

Accepted Answer

A)  $f ( x ) = ( x - 2 ) ( x + 2 ) ( x + 3 - i ) ( x + 3 + i )$ 
B)  $f ( x ) = ( x - 3 ) ( x + 3 ) ( x - 1 - 2 i ) ( x - 1 + 2 i )$ 
C)  $f ( x ) = ( x - 1 ) ( x + 1 ) ( x + 3 - 2 i ) ( x + 3 + 2 i )$ 
D)  $f ( x ) = ( x - 3 i ) ( x + 3 i ) ( x - 1 - 2 i ) ( x - 1 + 2 i )$ 
E)  $f ( x ) = ( x - i ) ( x + i ) ( x + 3 - 2 i ) ( x + 3 + 2 i )$ 
A)  $f ( x ) = ( x - 2 ) ( x + 2 ) ( x + 3 - i ) ( x + 3 + i )$ 
B)  $f ( x ) = ( x - 3 ) ( x + 3 ) ( x - 1 - 2 i ) ( x - 1 + 2 i )$ 
C)  $f ( x ) = ( x - 1 ) ( x + 1 ) ( x + 3 - 2 i ) ( x + 3 + 2 i )$ 
D)  $f ( x ) = ( x - 3 i ) ( x + 3 i ) ( x - 1 - 2 i ) ( x - 1 + 2 i )$ 
E)  $f ( x ) = ( x - i ) ( x + i ) ( x + 3 - 2 i ) ( x + 3 + 2 i )$

Question 11

Sketch the graph of the quadratic function below.
$h(x)=-x^{2}-4 x-1$

Accepted Answer

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

Question 12

Find the zeros of the function below algebraically, if any exist.
$$f ( x ) = x ^ { 4 } + 8 x ^ { 2 } + 15$$

Accepted Answer

A)  $- \sqrt { 5 } , - \sqrt { 3 } , \sqrt { 3 }$, and $\sqrt { 5 }$ 
B)  $- \sqrt { 3 } , 0$, and $\sqrt { 3 }$ 
C)  $- \sqrt { 3 }$ and $\sqrt { 3 }$ 
D)  $- \sqrt { 5 }$ and $\sqrt { 5 }$ 
E)  No zeros exist. 
A)  $- \sqrt { 5 } , - \sqrt { 3 } , \sqrt { 3 }$, and $\sqrt { 5 }$ 
B)  $- \sqrt { 3 } , 0$, and $\sqrt { 3 }$ 
C)  $- \sqrt { 3 }$ and $\sqrt { 3 }$ 
D)  $- \sqrt { 5 }$ and $\sqrt { 5 }$ 
E)  No zeros exist.

Question 13

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 }$ and determine the mutiplicity of each.

Accepted Answer

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

Question 14

Simplify $( - 4 + i ) ( 4 - 5 i )$ and write the answer in standard form.

Accepted Answer

A)  $16 + 24 i$ 
B)  $- 11 - 24 i$ 
C)  $- 16 + 24 i$ 
D)  $- 16 - 21 i$ 
E)  $- 11 + 24 i$ 
A)  $16 + 24 i$ 
B)  $- 11 - 24 i$ 
C)  $- 16 + 24 i$ 
D)  $- 16 - 21 i$ 
E)  $- 11 + 24 i$

Question 15

If $x = 4$ is a root of $x ^ { 3 } + 5 x ^ { 2 } - 16 x - 80 = 0$, use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Accepted Answer

A)  $( x - 5 ) ( x - 4 ) ( x + 4 ) ; x = 5,4 , - 4$ 
B)  $( x + 5 ) ( x - 4 ) ( x + 4 ) ; x = - 5,4 , - 4$ 
C)  $( x + 5 ) ( x - 4 ) ^ { 2 } ; x = - 5,4$ 
D)  $( x + 5 ) ^ { 2 } ( x - 4 ) ; x = - 5,4$ 
E)  $( x + 5 ) ( x - 5 ) ( x + 4 ) ; x = - 5,5 , - 4$ 
A)  $( x - 5 ) ( x - 4 ) ( x + 4 ) ; x = 5,4 , - 4$ 
B)  $( x + 5 ) ( x - 4 ) ( x + 4 ) ; x = - 5,4 , - 4$ 
C)  $( x + 5 ) ( x - 4 ) ^ { 2 } ; x = - 5,4$ 
D)  $( x + 5 ) ^ { 2 } ( x - 4 ) ; x = - 5,4$ 
E)  $( x + 5 ) ( x - 5 ) ( x + 4 ) ; x = - 5,5 , - 4$

Question 16

Find the zeros of the function below algebraically, if any exist.
$$f ( t ) = \frac { 1 } { 6 } t ^ { 4 } - \frac { 27 } { 2 }$$

Accepted Answer

A)  $- 3 , - 1,1$, and 3 
B)  $- 3$ and 3 
C)  $- 6$ and 6 
D)  $- 6 , - 1,1$, and 6 
E)  No zeros exist. 
A)  $- 3 , - 1,1$, and 3 
B)  $- 3$ and 3 
C)  $- 6$ and 6 
D)  $- 6 , - 1,1$, and 6 
E)  No zeros exist.

Question 17

Suppose the IQ scores $( y$, rounded to the nearest $10 )$ for a group of people are summarized in the table below. Use the regression feature of a graphing utility to find a quadratic function of the form $y = a x ^ { 2 } + b x + c$ for the data.
$\begin{array}{|c|c|}
\hline \text { IQ Score } & \text { Number of People } \
\hline \boldsymbol{y} & \boldsymbol{x} \
\hline 70 & 53 \
\hline 80 & 72 \
\hline 90 & 93 \
\hline 100 & 90 \
\hline 110 & 78 \
\hline 120 & 47 \
\hline 130 & 16 \
\hline
\end{array}$

Accepted Answer

A)  $y = - 0.04 x ^ { 2 } + 14.93 x - 404.96$ 
B)  $y = - 0.06 x ^ { 2 } + 11.94 x - 476.43$ 
C)  $y = - 0.08 x ^ { 2 } + 10.87 x - 500.25$ 
D)  $y = - 0.07 x ^ { 2 } + 13.5 x - 452.61$ 
E)  $y = - 0.09 x ^ { 2 } + 8.48 x - 547.89$ 
A)  $y = - 0.04 x ^ { 2 } + 14.93 x - 404.96$ 
B)  $y = - 0.06 x ^ { 2 } + 11.94 x - 476.43$ 
C)  $y = - 0.08 x ^ { 2 } + 10.87 x - 500.25$ 
D)  $y = - 0.07 x ^ { 2 } + 13.5 x - 452.61$ 
E)  $y = - 0.09 x ^ { 2 } + 8.48 x - 547.89$

Question 18

Use synthetic division to divide.
$$\left( 6 + 5 x ^ { 3 } + 23 x + 22 x ^ { 2 } \right) \div ( x + 3 )$$

Accepted Answer

A)  $5 x ^ { 2 } + 8 x + 3$ 
B)  $5 x ^ { 2 } + 17 x + 10$ 
C)  $5 x ^ { 2 } + 5 x + 6$ 
D)  $5 x ^ { 2 } + 7 x + 2$ 
E)  $5 x ^ { 2 } + 7 x + 5$ 
A)  $5 x ^ { 2 } + 8 x + 3$ 
B)  $5 x ^ { 2 } + 17 x + 10$ 
C)  $5 x ^ { 2 } + 5 x + 6$ 
D)  $5 x ^ { 2 } + 7 x + 2$ 
E)  $5 x ^ { 2 } + 7 x + 5$

Question 19

A polynomial function $f$ has degree 3 , the zeros below, and a solution point of $f ( 1 ) = - 96$. Write $f$ in completely factored form.
$- 2 , - 3 + 4 i$

Accepted Answer

A)  $f ( x ) = ( x + 3 ) ( x + 2 - 4 i ) ( x + 2 + 4 i )$ 
B)  $f ( x ) = - ( x + 2 ) ( x - 4 - 3 i ) ( x - 4 + 3 i )$ 
C)  $f ( x ) = ( x + 2 ) ( x - 4 - 3 i ) ( x - 4 + 3 i )$ 
D)  $f ( x ) = - ( x + 2 ) ( x + 3 - 4 i ) ( x + 3 + 4 i )$ 
E)  $f ( x ) = ( x + 2 ) ( x + 3 - 4 i ) ( x + 3 + 4 i )$ 
A)  $f ( x ) = ( x + 3 ) ( x + 2 - 4 i ) ( x + 2 + 4 i )$ 
B)  $f ( x ) = - ( x + 2 ) ( x - 4 - 3 i ) ( x - 4 + 3 i )$ 
C)  $f ( x ) = ( x + 2 ) ( x - 4 - 3 i ) ( x - 4 + 3 i )$ 
D)  $f ( x ) = - ( x + 2 ) ( x + 3 - 4 i ) ( x + 3 + 4 i )$ 
E)  $f ( x ) = ( x + 2 ) ( x + 3 - 4 i ) ( x + 3 + 4 i )$

Question 20

Find a polynomial function with following characteristics.
Degree: 4
Zero: 4 , multiplicity: 2
Zero: -3 , multiplicity: 2
Falls to the left,
Falls to the right
Absolute value of the leading coefficient is one

Accepted Answer

A)  $y = x ^ { 4 } + x ^ { 3 } - 23 x ^ { 2 } + 24 x - 12$ 
B)  $y = - x ^ { 4 } + x ^ { 3 } - 48 x ^ { 2 } + 9$ 
C)  $y = x ^ { 4 } - 6 x ^ { 3 } - 18 x ^ { 2 } + 25 x + 48$ 
D)  $y = - x ^ { 4 } + 2 x ^ { 3 } + 23 x ^ { 2 } - 24 x - 144$ 
E)  $y = - x ^ { 4 } + 2 x ^ { 3 } - 24 x - 36$ 
A)  $y = x ^ { 4 } + x ^ { 3 } - 23 x ^ { 2 } + 24 x - 12$ 
B)  $y = - x ^ { 4 } + x ^ { 3 } - 48 x ^ { 2 } + 9$ 
C)  $y = x ^ { 4 } - 6 x ^ { 3 } - 18 x ^ { 2 } + 25 x + 48$ 
D)  $y = - x ^ { 4 } + 2 x ^ { 3 } + 23 x ^ { 2 } - 24 x - 144$ 
E)  $y = - x ^ { 4 } + 2 x ^ { 3 } - 24 x - 36$

Determine the zeros (if any) of the rational function $f ( x ) = \frac { x ^ { 2 } - 64 } { x + 5 }$ .

If $x = - 1$ is a root of $x ^ { 3 } + 2 x ^ { 2 } - x - 2 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Write $f ( x ) = x ^ { 4 } - 12 x ^ { 3 } + 59 x ^ { 2 } - 138 x + 130$ as a product of linear factors.

If $f ( x ) = 4 x ^ { 2 } - 2 x - 7$ , use synthetic division to evaluate $f \left( \frac { 7 } { 8 } \right)$ .

Find the quadratic function $f$ whose graph intersects the $x$ -axis at $( - 7,0 )$ and $( 1,0 )$ and the $y$ -axis at $( 0 , - 14 )$ .

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } - 80 x ^ { 2 } + 1024$ and determine the mutiplicity of each.

Using the factors $( - 5 x + 2 )$ and $( x - 1 )$ , find the remaining factor(s) of $f ( x ) = 10 x ^ { 4 } + 31 x ^ { 3 } - 84 x ^ { 2 } + 53 x - 10$ and write the polynomial in fully factored form.

Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 16 }$ .

Write the polynomial in completely factored form. (Hint: One factor is $x ^ { 2 } + 1$ .) $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + 14 x ^ { 2 } + 6 x + 13$

Sketch the graph of the quadratic function below. $h(x)=-x^{2}-4 x-1$

Find the zeros of the function below algebraically, if any exist. $f ( x ) = x ^ { 4 } + 8 x ^ { 2 } + 15$

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 }$ and determine the mutiplicity of each.

Simplify $( - 4 + i ) ( 4 - 5 i )$ and write the answer in standard form.

If $x = 4$ is a root of $x ^ { 3 } + 5 x ^ { 2 } - 16 x - 80 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Find the zeros of the function below algebraically, if any exist. $f ( t ) = \frac { 1 } { 6 } t ^ { 4 } - \frac { 27 } { 2 }$

Use synthetic division to divide. $\left( 6 + 5 x ^ { 3 } + 23 x + 22 x ^ { 2 } \right) \div ( x + 3 )$

A polynomial function $f$ has degree 3 , the zeros below, and a solution point of $f ( 1 ) = - 96$ . Write $f$ in completely factored form. $- 2 , - 3 + 4 i$

Find a polynomial function with following characteristics. Degree: 4 Zero: 4 , multiplicity: 2 Zero: -3 , multiplicity: 2 Falls to the left, Falls to the right Absolute value of the leading coefficient is one

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Review of Graphs, Equations, and Inequalities

Filters

Exam 2: Polynomial and Rational Functions

Determine the zeros (if any) of the rational function f(x)=x2−64x+5f ( x ) = \frac { x ^ { 2 } - 64 } { x + 5 }f(x)=x+5x2−64​ .

If x=−1x = - 1x=−1 is a root of x3+2x2−x−2=0x ^ { 3 } + 2 x ^ { 2 } - x - 2 = 0x3+2x2−x−2=0 , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Write f(x)=x4−12x3+59x2−138x+130f ( x ) = x ^ { 4 } - 12 x ^ { 3 } + 59 x ^ { 2 } - 138 x + 130f(x)=x4−12x3+59x2−138x+130 as a product of linear factors.

Which of the given graphs is the graph of the polynomial function below? h(x)=x5−32x3−12xh ( x ) = x ^ { 5 } - \frac { 3 } { 2 } x ^ { 3 } - \frac { 1 } { 2 } xh(x)=x5−23​x3−21​x Graph 1: Graph 2 : Graph 3 : Graph 4 : Graph 5 :

If f(x)=4x2−2x−7f ( x ) = 4 x ^ { 2 } - 2 x - 7f(x)=4x2−2x−7 , use synthetic division to evaluate f(78)f \left( \frac { 7 } { 8 } \right)f(87​) .

Find the quadratic function fff whose graph intersects the xxx -axis at (−7,0)( - 7,0 )(−7,0) and (1,0)( 1,0 )(1,0) and the yyy -axis at (0,−14)( 0 , - 14 )(0,−14) .

Find all real zeros of the polynomial f(x)=x4−80x2+1024f ( x ) = x ^ { 4 } - 80 x ^ { 2 } + 1024f(x)=x4−80x2+1024 and determine the mutiplicity of each.

Using the factors (−5x+2)( - 5 x + 2 )(−5x+2) and (x−1)( x - 1 )(x−1) , find the remaining factor(s) of f(x)=10x4+31x3−84x2+53x−10f ( x ) = 10 x ^ { 4 } + 31 x ^ { 3 } - 84 x ^ { 2 } + 53 x - 10f(x)=10x4+31x3−84x2+53x−10 and write the polynomial in fully factored form.

Determine the equations of any horizontal and vertical asymptotes of f(x)=x2x2+16f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 16 }f(x)=x2+16x2​ .

Write the polynomial in completely factored form. (Hint: One factor is x2+1x ^ { 2 } + 1x2+1 .) f(x)=x4+6x3+14x2+6x+13f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + 14 x ^ { 2 } + 6 x + 13f(x)=x4+6x3+14x2+6x+13

Sketch the graph of the quadratic function below. h(x)=−x2−4x−1h(x)=-x^{2}-4 x-1h(x)=−x2−4x−1

Find the zeros of the function below algebraically, if any exist. f(x)=x4+8x2+15f ( x ) = x ^ { 4 } + 8 x ^ { 2 } + 15f(x)=x4+8x2+15

Find all real zeros of the polynomial f(x)=x4+8x3+12x2f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 }f(x)=x4+8x3+12x2 and determine the mutiplicity of each.

Simplify (−4+i)(4−5i)( - 4 + i ) ( 4 - 5 i )(−4+i)(4−5i) and write the answer in standard form.

If x=4x = 4x=4 is a root of x3+5x2−16x−80=0x ^ { 3 } + 5 x ^ { 2 } - 16 x - 80 = 0x3+5x2−16x−80=0 , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Find the zeros of the function below algebraically, if any exist. f(t)=16t4−272f ( t ) = \frac { 1 } { 6 } t ^ { 4 } - \frac { 27 } { 2 }f(t)=61​t4−227​

Use synthetic division to divide. (6+5x3+23x+22x2)÷(x+3)\left( 6 + 5 x ^ { 3 } + 23 x + 22 x ^ { 2 } \right) \div ( x + 3 )(6+5x3+23x+22x2)÷(x+3)

A polynomial function fff has degree 3 , the zeros below, and a solution point of f(1)=−96f ( 1 ) = - 96f(1)=−96 . Write fff in completely factored form. −2,−3+4i- 2 , - 3 + 4 i−2,−3+4i

Find a polynomial function with following characteristics. Degree: 4 Zero: 4 , multiplicity: 2 Zero: -3 , multiplicity: 2 Falls to the left, Falls to the right Absolute value of the leading coefficient is one

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Review of Graphs, Equations, and Inequalities

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Determine the zeros (if any) of the rational function $f ( x ) = \frac { x ^ { 2 } - 64 } { x + 5 }$ .

If $x = - 1$ is a root of $x ^ { 3 } + 2 x ^ { 2 } - x - 2 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Write $f ( x ) = x ^ { 4 } - 12 x ^ { 3 } + 59 x ^ { 2 } - 138 x + 130$ as a product of linear factors.

If $f ( x ) = 4 x ^ { 2 } - 2 x - 7$ , use synthetic division to evaluate $f \left( \frac { 7 } { 8 } \right)$ .

Find the quadratic function $f$ whose graph intersects the $x$ -axis at $( - 7,0 )$ and $( 1,0 )$ and the $y$ -axis at $( 0 , - 14 )$ .

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } - 80 x ^ { 2 } + 1024$ and determine the mutiplicity of each.

Using the factors $( - 5 x + 2 )$ and $( x - 1 )$ , find the remaining factor(s) of $f ( x ) = 10 x ^ { 4 } + 31 x ^ { 3 } - 84 x ^ { 2 } + 53 x - 10$ and write the polynomial in fully factored form.

Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 16 }$ .

Write the polynomial in completely factored form. (Hint: One factor is $x ^ { 2 } + 1$ .) $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + 14 x ^ { 2 } + 6 x + 13$

Sketch the graph of the quadratic function below. $h(x)=-x^{2}-4 x-1$

Find the zeros of the function below algebraically, if any exist. $f ( x ) = x ^ { 4 } + 8 x ^ { 2 } + 15$

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 }$ and determine the mutiplicity of each.

Simplify $( - 4 + i ) ( 4 - 5 i )$ and write the answer in standard form.

If $x = 4$ is a root of $x ^ { 3 } + 5 x ^ { 2 } - 16 x - 80 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Find the zeros of the function below algebraically, if any exist. $f ( t ) = \frac { 1 } { 6 } t ^ { 4 } - \frac { 27 } { 2 }$

Use synthetic division to divide. $\left( 6 + 5 x ^ { 3 } + 23 x + 22 x ^ { 2 } \right) \div ( x + 3 )$

A polynomial function $f$ has degree 3 , the zeros below, and a solution point of $f ( 1 ) = - 96$ . Write $f$ in completely factored form. $- 2 , - 3 + 4 i$