Question 1

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate. 
 $- 14 + \sqrt { 13 } i$

Accepted Answer

A)   $- 14 - \sqrt { 13 } i , 209$ 
B)   $14 - \sqrt { 13 } i , 209$ 
C)   $- 14 + \sqrt { 13 } i , 209$ 
D)   $14 + \sqrt { 13 } i , 209$ 
E)   $- 13 - \sqrt { 14 } i , 209$ 
A)   $- 14 - \sqrt { 13 } i , 209$ 
B)   $14 - \sqrt { 13 } i , 209$ 
C)   $- 14 + \sqrt { 13 } i , 209$ 
D)   $14 + \sqrt { 13 } i , 209$ 
E)   $- 13 - \sqrt { 14 } i , 209$

Question 2

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 12 x ^ { 3 } + 27 x ^ { 2 }$ and determine the multiplicity of each.

Accepted Answer

A)  $x = 0 \text {, multiplicity } 1 ; x = 9 , \text { multiplicity } 1 ; x = - 9 , \text { multiplicity } 1 ; x = 3 \text {, multiplicity } 1$ 
B)  $x = 0 \text {, multiplicity } 2 ; x = 9 \text {, multiplicity } 1 ; x = 3 \text {, multiplicity } 1$ 
C)  $x = 0 \text {, multiplicity } 2 ; x = - 9 \text {, multiplicity } 1 ; x = - 3 \text {, multiplicity } 1$ 
D)  $x = 9 , \text { multiplicity } 2 ; x = 3 , \text { multiplicity } 2$ 
E)  $x = 0 \text {, multiplicity } 1 ; x = 9 , \text { multiplicity } 1 ; x = - 9 , \text { multiplicity } 1 ; x = 3 \text {, multiplicity } 1$. 
A)  $x = 0 \text {, multiplicity } 1 ; x = 9 , \text { multiplicity } 1 ; x = - 9 , \text { multiplicity } 1 ; x = 3 \text {, multiplicity } 1$ 
B)  $x = 0 \text {, multiplicity } 2 ; x = 9 \text {, multiplicity } 1 ; x = 3 \text {, multiplicity } 1$ 
C)  $x = 0 \text {, multiplicity } 2 ; x = - 9 \text {, multiplicity } 1 ; x = - 3 \text {, multiplicity } 1$ 
D)  $x = 9 , \text { multiplicity } 2 ; x = 3 , \text { multiplicity } 2$ 
E)  $x = 0 \text {, multiplicity } 1 ; x = 9 , \text { multiplicity } 1 ; x = - 9 , \text { multiplicity } 1 ; x = 3 \text {, multiplicity } 1$.

Question 3

Perform the addition or subtraction and write the result in standard form.  
  $( 12 - i ) - ( 7 - i )$

Accepted Answer

A) 5 
B) 7 
C) 9 
D) 8 
E)  6 
A) 5 
B) 7 
C) 9 
D) 8 
E)  6

Question 4

Solve the inequality and graph the solution on the real number line. 
 $\frac { 1 } { x } \geq \frac { 1 } { x + 2 }$

Accepted Answer

A)  $( - \infty , - 2 ) \cap ( 0 , \infty )$     
B)  $( - \infty , - 2 ) \cup ( 0 , \infty )$   
C)  $( - \infty , 2 ) \cap ( 0 , \infty )$   
D)  $( \infty , 2 ) \cup ( 0 , \infty )$   
E)  $( - \infty , 2 ) \cup ( 0 , \infty )$   
A)  $( - \infty , - 2 ) \cap ( 0 , \infty )$     
B)  $( - \infty , - 2 ) \cup ( 0 , \infty )$   
C)  $( - \infty , 2 ) \cap ( 0 , \infty )$   
D)  $( \infty , 2 ) \cup ( 0 , \infty )$   
E)  $( - \infty , 2 ) \cup ( 0 , \infty )$

Question 5

Find the key numbers of the expression. 
 $\frac { 1 } { x - 7 } + 1$

Accepted Answer

A) -6, 7 
B) 6, 7, 1 
C) -6, -7 
D) 6, 7 
E) 6, -7 
A) -6, 7 
B) 6, 7, 1 
C) -6, -7 
D) 6, 7 
E) 6, -7

Question 6

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of f(x) = x5 + 2x.

Accepted Answer

A) 1 positive real; 3 negative reals or 1 negative real 
B) no positive reals; no negative reals 
C) 1 positive real; 5 negative reals or 3 negative reals or 1 negative real 
D) 5 positive reals or 3 positive reals or 1 positive real; no negative reals 
E) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real 
A) 1 positive real; 3 negative reals or 1 negative real 
B) no positive reals; no negative reals 
C) 1 positive real; 5 negative reals or 3 negative reals or 1 negative real 
D) 5 positive reals or 3 positive reals or 1 positive real; no negative reals 
E) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real

Question 7

Solve: $x ^ { 2 } - 2 x - 15 < 0$

Accepted Answer

A)  $( - \infty , - 2 )$ 
B)  $( - 3 , \infty )$ 
C)  $( - 3,5 )$ 
D)  $( - \infty , 5 )$ 
E)  $( 5 , \infty )$ 
A)  $( - \infty , - 2 )$ 
B)  $( - 3 , \infty )$ 
C)  $( - 3,5 )$ 
D)  $( - \infty , 5 )$ 
E)  $( 5 , \infty )$

Question 8

Find real numbers a and b such that the equation is true. 
$a + b i = 2 + 6 i$

Accepted Answer

A)   $a = 4 , b = 8$ 
B)   $a = 6 , b = 10$ 
C)   $a = 2 , b = 6$ 
D)   $a = 3 , b = 2$ 
E)   $a = 5 , b = 9$ 
A)   $a = 4 , b = 8$ 
B)   $a = 6 , b = 10$ 
C)   $a = 2 , b = 6$ 
D)   $a = 3 , b = 2$ 
E)   $a = 5 , b = 9$

Question 9

Select the graph of the quadratic function $f ( x ) = x ^ { 2 } + 5$ .Identify the vertex and axis of symmetry.

Accepted Answer

A)      Vertex: (0, 1)Axis of symmetry: y-axis 
B)     Vertex: (0, 3)Axis of symmetry: y-axis 
C)     Vertex: (0, 4)Axis of symmetry: y-axis 
D)     Vertex: (0, 5)Axis of symmetry: y-axis 
E)     Vertex: (0, 2)Axis of symmetry: y-axis 
A)      Vertex: (0, 1)Axis of symmetry: y-axis 
B)     Vertex: (0, 3)Axis of symmetry: y-axis 
C)     Vertex: (0, 4)Axis of symmetry: y-axis 
D)     Vertex: (0, 5)Axis of symmetry: y-axis 
E)     Vertex: (0, 2)Axis of symmetry: y-axis

Question 10

Solve the inequality and graph the solution on the real number line. 
 $x ^ { 2 } + x < 12$

Accepted Answer

A)  $( - 4,3 )$   
B)  $( - 4,3 )$   
C)  $( 4,3 )$   
D)  $( - 4 , - 3 )$   
E)  $( - 4 , - 3 )$   
A)  $( - 4,3 )$   
B)  $( - 4,3 )$   
C)  $( 4,3 )$   
D)  $( - 4 , - 3 )$   
E)  $( - 4 , - 3 )$

Question 11

Write $f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 15 x + 28$ in the form f (x) = (x - k)q(x) when k = -3.

Accepted Answer

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

Question 12

Write the polynomial as the product of factors that are irreducible over the rationals.  
F(x) = x4 + 6x2 - 27

Accepted Answer

A)  $\left( x ^ { 2 } + 9 \right) \left( x ^ { 4 } - 3 \right)$ 
B)  $\left( x ^ { 2 } + 9 \right) \left( x ^ { 2 } - 3 \right)$ 
C)  $( x + 9 ) \left( x ^ { 2 } - 3 \right)$ 
D)  $( x + 6 ) \left( x ^ { 2 } - 3 \right)$ 
E)  $\left( x ^ { 2 } + 9 \right) ( x + \sqrt { 3 } ) ( x + \sqrt { 3 } )$ 
A)  $\left( x ^ { 2 } + 9 \right) \left( x ^ { 4 } - 3 \right)$ 
B)  $\left( x ^ { 2 } + 9 \right) \left( x ^ { 2 } - 3 \right)$ 
C)  $( x + 9 ) \left( x ^ { 2 } - 3 \right)$ 
D)  $( x + 6 ) \left( x ^ { 2 } - 3 \right)$ 
E)  $\left( x ^ { 2 } + 9 \right) ( x + \sqrt { 3 } ) ( x + \sqrt { 3 } )$

Question 13

Solve the inequality and graph the solution on the real number line. 
 $x ^ { 2 } - 10 x - 24 > 0$

Accepted Answer

A)  $( - \infty , - 2 ) \cup ( 12 , \infty )$   
B)  $( - \infty , - 2 ) \cap ( - 12 , \infty )$   
C)  $( - \infty , - 2 ) \cup ( - \infty , - 12 , )$   
D)  $( \infty , - 2 ) \cup [ 12 , \infty )$   
E)  $( - \infty , 2 ] \cup ( 12 , \infty )$   
A)  $( - \infty , - 2 ) \cup ( 12 , \infty )$   
B)  $( - \infty , - 2 ) \cap ( - 12 , \infty )$   
C)  $( - \infty , - 2 ) \cup ( - \infty , - 12 , )$   
D)  $( \infty , - 2 ) \cup [ 12 , \infty )$   
E)  $( - \infty , 2 ] \cup ( 12 , \infty )$

Question 14

Given 3 + i is a root, determine all other roots of f(x) = x4 - 12x3 + 59 x2 - 138x + 130.

Accepted Answer

A) x = 3 - i, 3 ± 2i 
B) x = 3 - i, 2 ± 3i 
C) x = 3 + i, 3 ± 2i​, 2 - i 
D) x = 3 - i, 2 ± i 
E) x = 3 - i, 3 - 2i​, 2 - i 
A) x = 3 - i, 3 ± 2i 
B) x = 3 - i, 2 ± 3i 
C) x = 3 + i, 3 ± 2i​, 2 - i 
D) x = 3 - i, 2 ± i 
E) x = 3 - i, 3 - 2i​, 2 - i

Question 15

Find a polynomial function with real coefficients that has the given zeros. ​
6, 2 + i
​

Accepted Answer

A) x3 - 10x2 - 29x - 30 
B) x3 + 10x2 + 29x - 30 
C) x3 - 10x2 + 29x - 30 
D) x3 - 10x2 + 29x + 30 
E) x3 + 10x2 + 29x + 30 
A) x3 - 10x2 - 29x - 30 
B) x3 + 10x2 + 29x - 30 
C) x3 - 10x2 + 29x - 30 
D) x3 - 10x2 + 29x + 30 
E) x3 + 10x2 + 29x + 30

Question 16

The total revenue R earned per day (in dollars) from a pet-sitting service is given by   $R ( p ) = - 10 p ^ { 2 } + 120 p$  
Where p is the price charged per pet (in dollars).
 
Find the price that will yield a maximum revenue.

Accepted Answer

A) $7.00 
B) $10.00 
C) $8.00 
D) $6.00 
E) $9.00 
A) $7.00 
B) $10.00 
C) $8.00 
D) $6.00 
E) $9.00

Question 17

If x = $\frac { 3 } { 5 }$ is a root of $25 x ^ { 3 } - 105 x ^ { 2 } + 99 x - 27 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Accepted Answer

A)  $( 5 x - 3 ) ( 5 x + 3 ) ( x - 3 )$ x = $\frac { 3 } { 5 }$ , $- \frac { 3 } { 5 }$ , 3 
B)  $( 5 x + 3 ) ^ { 2 } ( x - 3 )$ x = $- \frac { 3 } { 5 }$ , 3 
C)   $( 5 x - 3 ) ( x - 3 ) ^ { 2 }$ x = $\frac { 3 } { 5 }$ , 3 
D)  $( 5 x + 3 ) ( x - 3 ) ^ { 2 }$ x = $- \frac { 3 } { 5 }$ , 3 
E)  $( 5 x - 3 ) ^ { 2 } ( x - 3 )$ x = $\frac { 3 } { 5 }$ , 3 
A)  $( 5 x - 3 ) ( 5 x + 3 ) ( x - 3 )$ x = $\frac { 3 } { 5 }$ , $- \frac { 3 } { 5 }$ , 3 
B)  $( 5 x + 3 ) ^ { 2 } ( x - 3 )$ x = $- \frac { 3 } { 5 }$ , 3 
C)   $( 5 x - 3 ) ( x - 3 ) ^ { 2 }$ x = $\frac { 3 } { 5 }$ , 3 
D)  $( 5 x + 3 ) ( x - 3 ) ^ { 2 }$ x = $- \frac { 3 } { 5 }$ , 3 
E)  $( 5 x - 3 ) ^ { 2 } ( x - 3 )$ x = $\frac { 3 } { 5 }$ , 3

Question 18

Write the complex number in standard form.  $\sqrt { - 17.64 }$

Accepted Answer

A) 17.64i 
B) 4.2i 
C)  7.2i 
D) -4.2i 
E) -17.64i 
A) 17.64i 
B) 4.2i 
C)  7.2i 
D) -4.2i 
E) -17.64i

Question 19

Write the quotient in standard form.
 $- \frac { 20 } { 5 i }$

Accepted Answer

A)  4i 
B)  $\frac { 4 } { i }$ 
C)   $- \frac { i } { 4 }$ 
D)   -4i
E  $- \frac { 4 } { i }$ 
A)  4i 
B)  $\frac { 4 } { i }$ 
C)   $- \frac { i } { 4 }$ 
D)   -4i
E  $- \frac { 4 } { i }$

Question 20

Determine the vertex of the graph of the quadratic function $f ( x ) = x ^ { 2 } + 5 x + \frac { 29 } { 4 }$ .

Accepted Answer

A)  $\left( \frac { 5 } { 2 } , \frac { 29 } { 4 } \right)$ 
B)  $\left( \frac { 5 } { 4 } , \frac { 21 } { 4 } \right)$ 
C)  $\left( - \frac { 5 } { 2 } , 1 \right)$ 
D)  $\left( - \frac { 5 } { 2 } , \frac { 27 } { 2 } \right)$ 
E)  $\left( 5 , \frac { 29 } { 4 } \right)$ 
A)  $\left( \frac { 5 } { 2 } , \frac { 29 } { 4 } \right)$ 
B)  $\left( \frac { 5 } { 4 } , \frac { 21 } { 4 } \right)$ 
C)  $\left( - \frac { 5 } { 2 } , 1 \right)$ 
D)  $\left( - \frac { 5 } { 2 } , \frac { 27 } { 2 } \right)$ 
E)  $\left( 5 , \frac { 29 } { 4 } \right)$

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate. $- 14 + \sqrt { 13 } i$

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 12 x ^ { 3 } + 27 x ^ { 2 }$ and determine the multiplicity of each.

Perform the addition or subtraction and write the result in standard form. $( 12 - i ) - ( 7 - i )$

Solve the inequality and graph the solution on the real number line. $\frac { 1 } { x } \geq \frac { 1 } { x + 2 }$

Find the key numbers of the expression. $\frac { 1 } { x - 7 } + 1$

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of f(x) = x⁵ + 2x.

Solve: $x ^ { 2 } - 2 x - 15 < 0$

Find real numbers a and b such that the equation is true. $a + b i = 2 + 6 i$

Select the graph of the quadratic function $f ( x ) = x ^ { 2 } + 5$ .Identify the vertex and axis of symmetry.

Solve the inequality and graph the solution on the real number line. $x ^ { 2 } + x < 12$

Write $f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 15 x + 28$ in the form f (x) = (x - k)q(x) when k = -3.

Write the polynomial as the product of factors that are irreducible over the rationals. F(x) = x⁴ + 6x² - 27

Solve the inequality and graph the solution on the real number line. $x ^ { 2 } - 10 x - 24 > 0$

Given 3 + i is a root, determine all other roots of f(x) = x⁴ - 12x³ + 59 x² - 138x + 130.

Find a polynomial function with real coefficients that has the given zeros. 6, 2 + i

The total revenue R earned per day (in dollars) from a pet-sitting service is given by $R ( p ) = - 10 p ^ { 2 } + 120 p$ Where p is the price charged per pet (in dollars). Find the price that will yield a maximum revenue.

If x = $\frac { 3 } { 5 }$ is a root of $25 x ^ { 3 } - 105 x ^ { 2 } + 99 x - 27 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Write the complex number in standard form. $\sqrt { - 17.64 }$

Write the quotient in standard form. $- \frac { 20 } { 5 i }$

Determine the vertex of the graph of the quadratic function $f ( x ) = x ^ { 2 } + 5 x + \frac { 29 } { 4 }$ .

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

Exam 2: Polynomial and Rational Functions

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate. −14+13i- 14 + \sqrt { 13 } i−14+13​i

Find all real zeros of the polynomial f(x)=x4+12x3+27x2f ( x ) = x ^ { 4 } + 12 x ^ { 3 } + 27 x ^ { 2 }f(x)=x4+12x3+27x2 and determine the multiplicity of each.

Perform the addition or subtraction and write the result in standard form. (12−i)−(7−i)( 12 - i ) - ( 7 - i )(12−i)−(7−i)

Solve the inequality and graph the solution on the real number line. 1x≥1x+2\frac { 1 } { x } \geq \frac { 1 } { x + 2 }x1​≥x+21​

Find the key numbers of the expression. 1x−7+1\frac { 1 } { x - 7 } + 1x−71​+1

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of f(x) = x5 + 2x.

Solve: x2−2x−15<0x ^ { 2 } - 2 x - 15 < 0x2−2x−15<0

Find real numbers a and b such that the equation is true. a+bi=2+6ia + b i = 2 + 6 ia+bi=2+6i

Select the graph of the quadratic function f(x)=x2+5f ( x ) = x ^ { 2 } + 5f(x)=x2+5 .Identify the vertex and axis of symmetry.

Solve the inequality and graph the solution on the real number line. x2+x<12x ^ { 2 } + x < 12x2+x<12

Write f(x)=x3+5x2+15x+28f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 15 x + 28f(x)=x3+5x2+15x+28 in the form f (x) = (x - k)q(x) when k = -3.

Write the polynomial as the product of factors that are irreducible over the rationals. F(x) = x4 + 6x2 - 27

Solve the inequality and graph the solution on the real number line. x2−10x−24>0x ^ { 2 } - 10 x - 24 > 0x2−10x−24>0

Given 3 + i is a root, determine all other roots of f(x) = x4 - 12x3 + 59 x2 - 138x + 130.

Find a polynomial function with real coefficients that has the given zeros. ​ 6, 2 + i ​

The total revenue R earned per day (in dollars) from a pet-sitting service is given by R(p)=−10p2+120pR ( p ) = - 10 p ^ { 2 } + 120 pR(p)=−10p2+120p Where p is the price charged per pet (in dollars). Find the price that will yield a maximum revenue.

If x = 35\frac { 3 } { 5 }53​ is a root of 25x3−105x2+99x−27=025 x ^ { 3 } - 105 x ^ { 2 } + 99 x - 27 = 025x3−105x2+99x−27=0 , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Write the complex number in standard form. −17.64\sqrt { - 17.64 }−17.64​

Write the quotient in standard form. −205i- \frac { 20 } { 5 i }−5i20​

Determine the vertex of the graph of the quadratic function f(x)=x2+5x+294f ( x ) = x ^ { 2 } + 5 x + \frac { 29 } { 4 }f(x)=x2+5x+429​ .

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

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate. $- 14 + \sqrt { 13 } i$

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 12 x ^ { 3 } + 27 x ^ { 2 }$ and determine the multiplicity of each.

Perform the addition or subtraction and write the result in standard form. $( 12 - i ) - ( 7 - i )$

Solve the inequality and graph the solution on the real number line. $\frac { 1 } { x } \geq \frac { 1 } { x + 2 }$

Find the key numbers of the expression. $\frac { 1 } { x - 7 } + 1$

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of f(x) = x⁵ + 2x.

Solve: $x ^ { 2 } - 2 x - 15 < 0$

Find real numbers a and b such that the equation is true. $a + b i = 2 + 6 i$

Select the graph of the quadratic function $f ( x ) = x ^ { 2 } + 5$ .Identify the vertex and axis of symmetry.

Solve the inequality and graph the solution on the real number line. $x ^ { 2 } + x < 12$

Write $f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 15 x + 28$ in the form f (x) = (x - k)q(x) when k = -3.

Write the polynomial as the product of factors that are irreducible over the rationals. F(x) = x⁴ + 6x² - 27

Solve the inequality and graph the solution on the real number line. $x ^ { 2 } - 10 x - 24 > 0$

Given 3 + i is a root, determine all other roots of f(x) = x⁴ - 12x³ + 59 x² - 138x + 130.

Find a polynomial function with real coefficients that has the given zeros. 6, 2 + i

The total revenue R earned per day (in dollars) from a pet-sitting service is given by $R ( p ) = - 10 p ^ { 2 } + 120 p$ Where p is the price charged per pet (in dollars). Find the price that will yield a maximum revenue.

If x = $\frac { 3 } { 5 }$ is a root of $25 x ^ { 3 } - 105 x ^ { 2 } + 99 x - 27 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Write the complex number in standard form. $\sqrt { - 17.64 }$

Write the quotient in standard form. $- \frac { 20 } { 5 i }$

Determine the vertex of the graph of the quadratic function $f ( x ) = x ^ { 2 } + 5 x + \frac { 29 } { 4 }$ .