Question 1

Find all the rational zeros of the function $f ( x ) = 3 x ^ { 4 } - 16 x ^ { 3 } - 59 x ^ { 2 } + 400 x - 4$

Accepted Answer

A)  $x = - 4,5 , - 5 , - \frac { 3 } { 4 }$ 
B)  $x = 3 , - 20,5$ 
C)  $x = 4,5 , - 5 , \frac { 4 } { 3 }$ 
D)  $x = - \frac { 4 } { 5 } , \frac { 5 } { 3 } , \frac { 4 } { 3 } , - 5$ 
E)  $\quad x = 3 , - 20 , \frac { 5 } { 3 } , \frac { 4 } { 3 }$ . 
A)  $x = - 4,5 , - 5 , - \frac { 3 } { 4 }$ 
B)  $x = 3 , - 20,5$ 
C)  $x = 4,5 , - 5 , \frac { 4 } { 3 }$ 
D)  $x = - \frac { 4 } { 5 } , \frac { 5 } { 3 } , \frac { 4 } { 3 } , - 5$ 
E)  $\quad x = 3 , - 20 , \frac { 5 } { 3 } , \frac { 4 } { 3 }$ .

Question 2

Find a polynomial function of the lowest degree with real coefficients that has the zeros below and whose leading coefficient is one.
$0,2,4 - i$

Accepted Answer

A)  $f ( x ) = x ^ { 4 } - 34 x ^ { 3 } + 32 x ^ { 2 } - 10 x$ 
B)  $f ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 33 x ^ { 2 } - 34 x$ 
C)  $f ( x ) = x ^ { 4 } + 32 x ^ { 3 } - 10 x ^ { 2 } - 34 x$ 
D)  $f ( x ) = x ^ { 4 } - 10 x ^ { 3 } - 34 x ^ { 2 } + 32 x$ 
E)  $f ( x ) = x ^ { 4 } + 32 x ^ { 3 } - 34 x ^ { 2 } - 10 x$ 
A)  $f ( x ) = x ^ { 4 } - 34 x ^ { 3 } + 32 x ^ { 2 } - 10 x$ 
B)  $f ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 33 x ^ { 2 } - 34 x$ 
C)  $f ( x ) = x ^ { 4 } + 32 x ^ { 3 } - 10 x ^ { 2 } - 34 x$ 
D)  $f ( x ) = x ^ { 4 } - 10 x ^ { 3 } - 34 x ^ { 2 } + 32 x$ 
E)  $f ( x ) = x ^ { 4 } + 32 x ^ { 3 } - 34 x ^ { 2 } - 10 x$

Question 3

Write the complex conjugate of the following complex number and then multiply the number by the complex conjugate. Write the result in standard form.
$1 + \sqrt { - 20 }$

Accepted Answer

A)  $1 - 20 i ; 19$ 
B)  $1 - 5 \sqrt { 2 } i ; 21$ 
C)  $- 1 - 2 \sqrt { 5 } i ; 21$ 
D)  $- 1 - 2 \sqrt { 5 } i ; 19$ 
E)  $1 - 2 \sqrt { 5 } i ; 21$ 
A)  $1 - 20 i ; 19$ 
B)  $1 - 5 \sqrt { 2 } i ; 21$ 
C)  $- 1 - 2 \sqrt { 5 } i ; 21$ 
D)  $- 1 - 2 \sqrt { 5 } i ; 19$ 
E)  $1 - 2 \sqrt { 5 } i ; 21$

Question 4

Which of the following is the graph of the given equation?
$f ( x ) = \frac { 2 - x } { x + 3 }$

Accepted Answer

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

Question 5

Use the regression feature of a graphing utility to find a quadratic model for the data below. 
$\begin{array}{|r|c|}
\hline x & y \
\hline-2 & -7.3 \
\hline-1 & -2 \
\hline 0 & -1 \
\hline 1 & -4.8 \
\hline 2 & -11.4 \
\hline 3 & -22.8 \
\hline 4 & -37.8 \
\hline
\end{array}$

Accepted Answer

A)  $y = - 1.91 x ^ { 2 } - 1.21 x - 1.57$ 
B)  $y = - 1.81 x ^ { 2 } - 1.15 x - 1.42$ 
C)  $y = - 2.21 x ^ { 2 } - 1.04 x - 1$ 
D)  $y = - 2.11 x ^ { 2 } - 0.99 x - 1.07$ 
E)  $y = - 2.01 x ^ { 2 } - 1.1 x - 1.28$ 
A)  $y = - 1.91 x ^ { 2 } - 1.21 x - 1.57$ 
B)  $y = - 1.81 x ^ { 2 } - 1.15 x - 1.42$ 
C)  $y = - 2.21 x ^ { 2 } - 1.04 x - 1$ 
D)  $y = - 2.11 x ^ { 2 } - 0.99 x - 1.07$ 
E)  $y = - 2.01 x ^ { 2 } - 1.1 x - 1.28$

Question 6

Find all the rational zeros of the function $f ( x ) = - 2 x ^ { 5 } - 11 x ^ { 4 } - 19 x ^ { 3 } - 17 x ^ { 2 } - 17 x - 6$.

Accepted Answer

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

Question 7

Determine whether the scatter plot could best be modeled by a linear model, a quadratic model, or neither.

Accepted Answer

A)  linear model 
B)  quadratic model 
C)  neither 
A)  linear model 
B)  quadratic model 
C)  neither

Question 8

Given $f ( x ) = \frac { 5 x + 4 } { 5 x ^ { 2 } + 4 x }$. Determine the domain of $f ( x )$ and find any vertical asymptotes.

Accepted Answer

A)  domain: all real numbers except $x = - \frac { 4 } { 5 }$ vertical asymptote: $x = 0$ 
B)  domain: all real numbers except $x = 0$ and $x = - \frac { 4 } { 5 }$
vertical asymptote: $x = 0$
domain: all real numbers 
C)  vertical asymptotes: $x = 0$ and $x = - \frac { 4 } { 5 }$ 
D)  domain: all real numbers except $x = 0$ and $x = \frac { 4 } { 5 }$
vertical asymptote: $x = 0$
domain: all real numbers except $x = \frac { 4 } { 5 }$ 
E) 
vertical asymptotes: $x = 0$ and $x = - \frac { 4 } { 5 }$. 
A)  domain: all real numbers except $x = - \frac { 4 } { 5 }$ vertical asymptote: $x = 0$ 
B)  domain: all real numbers except $x = 0$ and $x = - \frac { 4 } { 5 }$
vertical asymptote: $x = 0$
domain: all real numbers 
C)  vertical asymptotes: $x = 0$ and $x = - \frac { 4 } { 5 }$ 
D)  domain: all real numbers except $x = 0$ and $x = \frac { 4 } { 5 }$
vertical asymptote: $x = 0$
domain: all real numbers except $x = \frac { 4 } { 5 }$ 
E) 
vertical asymptotes: $x = 0$ and $x = - \frac { 4 } { 5 }$.

Question 9

Simplify $( \sqrt { - 3 } ) ^ { 9 }$ and write the answer in standard form.

Accepted Answer

A)  $- 81 \sqrt { 3 } i$ 
B)  $81 \sqrt { 3 } i$ 
C)  $6561 \sqrt { 3 } i$ 
D)  $81 \sqrt { 3 }$ 
E)  The expression cannot be simplified. 
A)  $- 81 \sqrt { 3 } i$ 
B)  $81 \sqrt { 3 } i$ 
C)  $6561 \sqrt { 3 } i$ 
D)  $81 \sqrt { 3 }$ 
E)  The expression cannot be simplified.

Question 10

The interest rates that banks charge to borrow money fluctuate with the economy. The interest rate charged by a bank in a certain country is given in the table below. Let $t$ represent the year, with $t = 0$ corresponding to 1986. Use the regression feature of a graphing utility to find a quadratic model of the form $y = a t ^ { 2 } + b t + c$ for the data.
$\begin{array}{|c|c|}
\hline \text { Year } & \text { Percent } \
\boldsymbol{t} & \boldsymbol{y} \
\hline 1986 & 12.4 \
\hline 1988 & 9.7 \
\hline 1990 & 7.3 \
\hline 1992 & 6.3 \
\hline 1994 & 9.7 \
\hline 1996 & 11.6 \
\hline
\end{array}$

Accepted Answer

A)  $y = - 2.13 t ^ { 2 } + 12.61 t + 0.21$ 
B)  $y = 12.61 t ^ { 2 } + 0.21 t - 2.13$ 
C)  $y = 0.21 t ^ { 2 } - 2.13 t + 12.61$ 
D)  $y = 0.17 t ^ { 2 } - 2.58 t + 10.59$ 
E)  $y = 0.25 t ^ { 2 } - 1.73 t + 14.37$ 
A)  $y = - 2.13 t ^ { 2 } + 12.61 t + 0.21$ 
B)  $y = 12.61 t ^ { 2 } + 0.21 t - 2.13$ 
C)  $y = 0.21 t ^ { 2 } - 2.13 t + 12.61$ 
D)  $y = 0.17 t ^ { 2 } - 2.58 t + 10.59$ 
E)  $y = 0.25 t ^ { 2 } - 1.73 t + 14.37$

Question 11

Find real numbers $a$ and $b$ such that the equation $a + b i = 10 - 12 i$ is true.

Accepted Answer

A)  $a = - 10 , b = 12$ 
B)  $a = 10 , b = 12$ 
C)  $a = - 10 , b = - 12$ 
D)  $a = 10 , b = - 12$ 
E)  $a = 22 , b = - 2$ 
A)  $a = - 10 , b = 12$ 
B)  $a = 10 , b = 12$ 
C)  $a = - 10 , b = - 12$ 
D)  $a = 10 , b = - 12$ 
E)  $a = 22 , b = - 2$

Question 12

Determine the value that $f ( x ) = \frac { 4 x - 6 } { x ^ { 2 } - 7 }$ approaches as $x$ increases and decreases in magnitude without bound.

Accepted Answer

A)  8 
B)  6 
C)  4 
D)  2 
E)  0 
A)  8 
B)  6 
C)  4 
D)  2 
E)  0

Question 13

Describe the right-hand and the left-hand behavior of the graph of $t ( x ) = - \frac { 4 } { 7 } \left( x ^ { 3 } + 5 x ^ { 2 } + 8 x + 1 \right)$.

Accepted Answer

A)  Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right. 
B)  Because the degree is odd and the leading coefficient is negative, the graph rises to the left and falls to the right. 
C)  Because the degree is odd and the leading coefficient is negative, the graph falls to the left and rises 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. 
A)  Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right. 
B)  Because the degree is odd and the leading coefficient is negative, the graph rises to the left and falls to the right. 
C)  Because the degree is odd and the leading coefficient is negative, the graph falls to the left and rises 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 14

Use long division to divide.
$$\left( x ^ { 3 } + 5 x ^ { 2 } + 36 x + 180 \right) \div ( x + 5 )$$

Accepted Answer

A)  $x ^ { 2 } + 30$ 
B)  $x ^ { 2 } + 10 x + 44 - \frac { 244 } { x + 5 }$ 
C)  $x ^ { 2 } + 10 x + 86 + \frac { 110 } { x + 5 }$ 
D)  $x ^ { 2 } + 10 x + 44$ 
E)  $x ^ { 2 } + 36$ 
A)  $x ^ { 2 } + 30$ 
B)  $x ^ { 2 } + 10 x + 44 - \frac { 244 } { x + 5 }$ 
C)  $x ^ { 2 } + 10 x + 86 + \frac { 110 } { x + 5 }$ 
D)  $x ^ { 2 } + 10 x + 44$ 
E)  $x ^ { 2 } + 36$

Question 15

Simplify $\frac { 4 + 3 i } { 5 + 2 i }$ and write the answer in standard form.

Accepted Answer

A)  $- \frac { 26 } { 29 } + \frac { 7 } { 29 } i$ 
B)  $\frac { 26 } { 29 } - \frac { 7 } { 29 } i$ 
C)  $\frac { 26 } { 29 } + \frac { 7 } { 29 } i$ 
D)  $\frac { 7 } { 29 } + \frac { 26 } { 29 } i$ 
E)  $\frac { 7 } { 29 } - \frac { 26 } { 29 } i$ 
A)  $- \frac { 26 } { 29 } + \frac { 7 } { 29 } i$ 
B)  $\frac { 26 } { 29 } - \frac { 7 } { 29 } i$ 
C)  $\frac { 26 } { 29 } + \frac { 7 } { 29 } i$ 
D)  $\frac { 7 } { 29 } + \frac { 26 } { 29 } i$ 
E)  $\frac { 7 } { 29 } - \frac { 26 } { 29 } i$

Question 16

Find the zeros of the function below algebraically, if any exist.
$ f(x)=2 x^{4}+10 x^{2}+12 $

Accepted Answer

A)  $- \sqrt { 3 } , - \sqrt { 2 } , \sqrt { 2 }$, and $\sqrt { 3 }$ 
B)  $- \sqrt { 3 } , 0$, and $\sqrt { 3 }$ 
C)  $- \sqrt { 3 }$ and $\sqrt { 3 }$ 
D)  $- \sqrt { 2 }$ and $\sqrt { 2 }$ 
E)  No zeros exist. 
A)  $- \sqrt { 3 } , - \sqrt { 2 } , \sqrt { 2 }$, and $\sqrt { 3 }$ 
B)  $- \sqrt { 3 } , 0$, and $\sqrt { 3 }$ 
C)  $- \sqrt { 3 }$ and $\sqrt { 3 }$ 
D)  $- \sqrt { 2 }$ and $\sqrt { 2 }$ 
E)  No zeros exist.

Question 17

Find a fifth degree polynomial function of the lowest degree that has the zeros below and whose leading coefficient is one.
$- 3 , - 1,0,1,3$

Accepted Answer

A)  $f ( x ) = x ^ { 5 } + 7 x ^ { 4 } - 19 x ^ { 3 } - 32 x ^ { 2 } + 48 x$ 
B)  $f ( x ) = x ^ { 5 } + 7 x ^ { 4 } - 19 x ^ { 3 } + 32 x ^ { 2 } + 48 x$ 
C)  $f ( x ) = x ^ { 5 } + 4 x ^ { 4 } - 13 x ^ { 3 } + 3 x ^ { 2 } + 12 x$ 
D)  $f ( x ) = x ^ { 5 } + 5 x ^ { 4 } - 13 x ^ { 3 } + 27 x ^ { 2 } + 36 x$ 
E)  $f ( x ) = x ^ { 5 } - 10 x ^ { 3 } + 9 x$ 
A)  $f ( x ) = x ^ { 5 } + 7 x ^ { 4 } - 19 x ^ { 3 } - 32 x ^ { 2 } + 48 x$ 
B)  $f ( x ) = x ^ { 5 } + 7 x ^ { 4 } - 19 x ^ { 3 } + 32 x ^ { 2 } + 48 x$ 
C)  $f ( x ) = x ^ { 5 } + 4 x ^ { 4 } - 13 x ^ { 3 } + 3 x ^ { 2 } + 12 x$ 
D)  $f ( x ) = x ^ { 5 } + 5 x ^ { 4 } - 13 x ^ { 3 } + 27 x ^ { 2 } + 36 x$ 
E)  $f ( x ) = x ^ { 5 } - 10 x ^ { 3 } + 9 x$

Question 18

Use long division to divide.
$$\left( 2 x ^ { 2 } + 11 x + 12 \right) \div ( x + 4 )$$

Accepted Answer

A)  $2 x + 19 + \frac { 88 } { x + 4 }$ 
B)  $2 x + 3$ 
C)  $2 x + 19 + \frac { 22 } { x + 4 }$ 
D)  $2 x + 22$ 
E)  $- 2 x - 3$ 
A)  $2 x + 19 + \frac { 88 } { x + 4 }$ 
B)  $2 x + 3$ 
C)  $2 x + 19 + \frac { 22 } { x + 4 }$ 
D)  $2 x + 22$ 
E)  $- 2 x - 3$

Question 19

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

Accepted Answer

A)  $x = - \sqrt { 5 } , x = \sqrt { 5 }$ 
B)  $x = - 2$ 
C)  $x = - \frac { 2 } { 5 } , x = \frac { 2 } { 5 }$ 
D)  $x = - 5 , x = 5$ 
E)  no zeros 
A)  $x = - \sqrt { 5 } , x = \sqrt { 5 }$ 
B)  $x = - 2$ 
C)  $x = - \frac { 2 } { 5 } , x = \frac { 2 } { 5 }$ 
D)  $x = - 5 , x = 5$ 
E)  no zeros

Question 20

The interest rates that banks charge to borrow money fluctuate with the economy. The interest rate charged by a bank in a certain country is given in the table below. Let $t$ represent the year, with $t = 0$ corresponding to 1986 . Use the regression feature of a graphing utility to find a quadratic model of the form $y = a t ^ { 2 } + b t + c$ for the data.
$\begin{array}{|c|c|}
\hline \text { Year } & \text { Percent } \
\boldsymbol{t} & \boldsymbol{y} \
\hline 1986 & 12.1 \
\hline 1988 & 10.1 \
\hline 1990 & 6.8 \
\hline 1992 & 6.6 \
\hline 1994 & 8.6 \
\hline 1996 & 12.0 \
\hline
\end{array}$

Accepted Answer

A)  $y = - 2.23 t ^ { 2 } + 12.61 t + 0.22$ 
B)  $y = 12.61 t ^ { 2 } + 0.22 t - 2.23$ 
C)  $y = 0.22 t ^ { 2 } - 2.23 t + 12.61$ 
D)  $y = 0.17 t ^ { 2 } - 2.69 t + 10.59$ 
E)  $y = 0.26 t ^ { 2 } - 1.8 t + 14.37$ 
A)  $y = - 2.23 t ^ { 2 } + 12.61 t + 0.22$ 
B)  $y = 12.61 t ^ { 2 } + 0.22 t - 2.23$ 
C)  $y = 0.22 t ^ { 2 } - 2.23 t + 12.61$ 
D)  $y = 0.17 t ^ { 2 } - 2.69 t + 10.59$ 
E)  $y = 0.26 t ^ { 2 } - 1.8 t + 14.37$

Find all the rational zeros of the function $f ( x ) = 3 x ^ { 4 } - 16 x ^ { 3 } - 59 x ^ { 2 } + 400 x - 4$

Find a polynomial function of the lowest degree with real coefficients that has the zeros below and whose leading coefficient is one. $0,2,4 - i$

Write the complex conjugate of the following complex number and then multiply the number by the complex conjugate. Write the result in standard form. $1 + \sqrt { - 20 }$

Which of the following is the graph of the given equation? $f ( x ) = \frac { 2 - x } { x + 3 }$

Use the regression feature of a graphing utility to find a quadratic model for the data below. x y -2 -7.3 -1 -2 0 -1 1 -4.8 2 -11.4 3 -22.8 4 -37.8

Find all the rational zeros of the function $f ( x ) = - 2 x ^ { 5 } - 11 x ^ { 4 } - 19 x ^ { 3 } - 17 x ^ { 2 } - 17 x - 6$ .

Determine whether the scatter plot could best be modeled by a linear model, a quadratic model, or neither.

Given $f ( x ) = \frac { 5 x + 4 } { 5 x ^ { 2 } + 4 x }$ . Determine the domain of $f ( x )$ and find any vertical asymptotes.

Simplify $( \sqrt { - 3 } ) ^ { 9 }$ and write the answer in standard form.

Find real numbers $a$ and $b$ such that the equation $a + b i = 10 - 12 i$ is true.

Determine the value that $f ( x ) = \frac { 4 x - 6 } { x ^ { 2 } - 7 }$ approaches as $x$ increases and decreases in magnitude without bound.

Describe the right-hand and the left-hand behavior of the graph of $t ( x ) = - \frac { 4 } { 7 } \left( x ^ { 3 } + 5 x ^ { 2 } + 8 x + 1 \right)$ .

Use long division to divide. $\left( x ^ { 3 } + 5 x ^ { 2 } + 36 x + 180 \right) \div ( x + 5 )$

Simplify $\frac { 4 + 3 i } { 5 + 2 i }$ and write the answer in standard form.

Find the zeros of the function below algebraically, if any exist. $f(x)=2 x^{4}+10 x^{2}+12$

Find a fifth degree polynomial function of the lowest degree that has the zeros below and whose leading coefficient is one. $- 3 , - 1,0,1,3$

Use long division to divide. $\left( 2 x ^ { 2 } + 11 x + 12 \right) \div ( x + 4 )$

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

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

Find all the rational zeros of the function f(x)=3x4−16x3−59x2+400x−4f ( x ) = 3 x ^ { 4 } - 16 x ^ { 3 } - 59 x ^ { 2 } + 400 x - 4f(x)=3x4−16x3−59x2+400x−4

Find a polynomial function of the lowest degree with real coefficients that has the zeros below and whose leading coefficient is one. 0,2,4−i0,2,4 - i0,2,4−i

Write the complex conjugate of the following complex number and then multiply the number by the complex conjugate. Write the result in standard form. 1+−201 + \sqrt { - 20 }1+−20​

Which of the following is the graph of the given equation? f(x)=2−xx+3f ( x ) = \frac { 2 - x } { x + 3 }f(x)=x+32−x​

Use the regression feature of a graphing utility to find a quadratic model for the data below. x y -2 -7.3 -1 -2 0 -1 1 -4.8 2 -11.4 3 -22.8 4 -37.8

Find all the rational zeros of the function f(x)=−2x5−11x4−19x3−17x2−17x−6f ( x ) = - 2 x ^ { 5 } - 11 x ^ { 4 } - 19 x ^ { 3 } - 17 x ^ { 2 } - 17 x - 6f(x)=−2x5−11x4−19x3−17x2−17x−6 .

Determine whether the scatter plot could best be modeled by a linear model, a quadratic model, or neither.

Given f(x)=5x+45x2+4xf ( x ) = \frac { 5 x + 4 } { 5 x ^ { 2 } + 4 x }f(x)=5x2+4x5x+4​ . Determine the domain of f(x)f ( x )f(x) and find any vertical asymptotes.

Simplify (−3)9( \sqrt { - 3 } ) ^ { 9 }(−3​)9 and write the answer in standard form.

Find real numbers aaa and bbb such that the equation a+bi=10−12ia + b i = 10 - 12 ia+bi=10−12i is true.

Determine the value that f(x)=4x−6x2−7f ( x ) = \frac { 4 x - 6 } { x ^ { 2 } - 7 }f(x)=x2−74x−6​ approaches as xxx increases and decreases in magnitude without bound.

Describe the right-hand and the left-hand behavior of the graph of t(x)=−47(x3+5x2+8x+1)t ( x ) = - \frac { 4 } { 7 } \left( x ^ { 3 } + 5 x ^ { 2 } + 8 x + 1 \right)t(x)=−74​(x3+5x2+8x+1) .

Use long division to divide. (x3+5x2+36x+180)÷(x+5)\left( x ^ { 3 } + 5 x ^ { 2 } + 36 x + 180 \right) \div ( x + 5 )(x3+5x2+36x+180)÷(x+5)

Simplify 4+3i5+2i\frac { 4 + 3 i } { 5 + 2 i }5+2i4+3i​ and write the answer in standard form.

Find the zeros of the function below algebraically, if any exist. f(x)=2x4+10x2+12 f(x)=2 x^{4}+10 x^{2}+12 f(x)=2x4+10x2+12

Find a fifth degree polynomial function of the lowest degree that has the zeros below and whose leading coefficient is one. −3,−1,0,1,3- 3 , - 1,0,1,3−3,−1,0,1,3

Use long division to divide. (2x2+11x+12)÷(x+4)\left( 2 x ^ { 2 } + 11 x + 12 \right) \div ( x + 4 )(2x2+11x+12)÷(x+4)

Determine the zeros (if any) of the rational function g(x)=5+2x2+5g ( x ) = 5 + \frac { 2 } { x ^ { 2 } + 5 }g(x)=5+x2+52​ .

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

Find all the rational zeros of the function $f ( x ) = 3 x ^ { 4 } - 16 x ^ { 3 } - 59 x ^ { 2 } + 400 x - 4$

Find a polynomial function of the lowest degree with real coefficients that has the zeros below and whose leading coefficient is one. $0,2,4 - i$

Write the complex conjugate of the following complex number and then multiply the number by the complex conjugate. Write the result in standard form. $1 + \sqrt { - 20 }$

Which of the following is the graph of the given equation? $f ( x ) = \frac { 2 - x } { x + 3 }$

Find all the rational zeros of the function $f ( x ) = - 2 x ^ { 5 } - 11 x ^ { 4 } - 19 x ^ { 3 } - 17 x ^ { 2 } - 17 x - 6$ .

Given $f ( x ) = \frac { 5 x + 4 } { 5 x ^ { 2 } + 4 x }$ . Determine the domain of $f ( x )$ and find any vertical asymptotes.

Simplify $( \sqrt { - 3 } ) ^ { 9 }$ and write the answer in standard form.

Find real numbers $a$ and $b$ such that the equation $a + b i = 10 - 12 i$ is true.

Determine the value that $f ( x ) = \frac { 4 x - 6 } { x ^ { 2 } - 7 }$ approaches as $x$ increases and decreases in magnitude without bound.

Describe the right-hand and the left-hand behavior of the graph of $t ( x ) = - \frac { 4 } { 7 } \left( x ^ { 3 } + 5 x ^ { 2 } + 8 x + 1 \right)$ .

Use long division to divide. $\left( x ^ { 3 } + 5 x ^ { 2 } + 36 x + 180 \right) \div ( x + 5 )$

Simplify $\frac { 4 + 3 i } { 5 + 2 i }$ and write the answer in standard form.

Find the zeros of the function below algebraically, if any exist. $f(x)=2 x^{4}+10 x^{2}+12$

Find a fifth degree polynomial function of the lowest degree that has the zeros below and whose leading coefficient is one. $- 3 , - 1,0,1,3$

Use long division to divide. $\left( 2 x ^ { 2 } + 11 x + 12 \right) \div ( x + 4 )$

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