Question 1

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

Accepted Answer

A) horizontal: y = 0 ; vertical: x = 4 
B) horizontal: y = -4 ; vertical: x = 0 
C) horizontal: x = 0; vertical: y = 4 
D) horizontal: x = 4 ; vertical: y = -1 
E) horizontal: y = 1 ; vertical: x = 4 
A) horizontal: y = 0 ; vertical: x = 4 
B) horizontal: y = -4 ; vertical: x = 0 
C) horizontal: x = 0; vertical: y = 4 
D) horizontal: x = 4 ; vertical: y = -1 
E) horizontal: y = 1 ; vertical: x = 4

Question 2

Find the vertex of the parabola. y = - x2 + 16x - 60

Accepted Answer

A) (-8, 4) 
B) (8, 4) 
C) (-8, -4) 
D) (8, -30) 
E) (4, 8) 
A) (-8, 4) 
B) (8, 4) 
C) (-8, -4) 
D) (8, -30) 
E) (4, 8)

Question 3

Use long division to divide. 
 $\left( 6 x ^ { 3 } - 27 x ^ { 2 } + 39 x - 18 \right) \div ( 3 x - 6 )$

Accepted Answer

A)  $2 x ^ { 2 } - 5 x + 3 , x \neq \frac { 6 } { 3 }$ 
B)  $2 x ^ { 2 } - 5 x - 3 , x \neq \frac { 6 } { 3 }$ 
C)  $- 2 x ^ { 2 } - 5 x + 3 , x \neq \frac { 6 } { 3 }$ 
D)  $2 x ^ { 2 } + 5 x + 3 , x \neq \frac { 6 } { 3 }$ 
E)  $2 x ^ { 2 } + 5 x - 3 , x \neq \frac { 6 } { 3 }$ 
A)  $2 x ^ { 2 } - 5 x + 3 , x \neq \frac { 6 } { 3 }$ 
B)  $2 x ^ { 2 } - 5 x - 3 , x \neq \frac { 6 } { 3 }$ 
C)  $- 2 x ^ { 2 } - 5 x + 3 , x \neq \frac { 6 } { 3 }$ 
D)  $2 x ^ { 2 } + 5 x + 3 , x \neq \frac { 6 } { 3 }$ 
E)  $2 x ^ { 2 } + 5 x - 3 , x \neq \frac { 6 } { 3 }$

Question 4

Solve the equation and write complex solutions in standard form.  
  $x ^ { 2 } - 18 x + 91 = 0$

Accepted Answer

A)   $x = 9 + \sqrt { 10 } i , 9 - \sqrt { 10 } i$ 
B)   $x = 10 + \sqrt { 2 } i , 10 - \sqrt { 2 } i$ 
C)   $x = 9 + \sqrt { 2 } i , 9 - \sqrt { 2 } i$ 
D)   $x = 10 + \sqrt { 10 } i , 10 - \sqrt { 10 } i$ 
E)   $x = 2 + \sqrt { 10 } i , 2 - \sqrt { 10 } i$ 
A)   $x = 9 + \sqrt { 10 } i , 9 - \sqrt { 10 } i$ 
B)   $x = 10 + \sqrt { 2 } i , 10 - \sqrt { 2 } i$ 
C)   $x = 9 + \sqrt { 2 } i , 9 - \sqrt { 2 } i$ 
D)   $x = 10 + \sqrt { 10 } i , 10 - \sqrt { 10 } i$ 
E)   $x = 2 + \sqrt { 10 } i , 2 - \sqrt { 10 } i$

Question 5

The cost C (in millions of dollars) removing p% the industrial and municipal pollutants discharged into a river is given by $C = \frac { 200 p } { 100 - p } , 0 \leq p < 100$ 
 Select the correct graph of the cost function.

Accepted Answer

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

Question 6

Find the zeros (if any) of the rational function. 
 $f ( x ) = 2 + \frac { 12 } { x ^ { 2 } + 2 }$

Accepted Answer

A) -2 
B) 2 
C) 8 
D) -8 
E) None 
A) -2 
B) 2 
C) 8 
D) -8 
E) None

Question 7

Find a polynomial with the given zeros.   $- 1,5 , - \sqrt { 7 } , \sqrt { 7 }$

Accepted Answer

A)  $x ^ { 5 } - 4 x ^ { 4 } - 12 x ^ { 3 } + 28 x ^ { 2 } + 35 x - 2$ 
B)  $x ^ { 4 } - 12 x ^ { 2 } + 35$ 
C)  $x ^ { 4 } - 12 x ^ { 3 } - 4 x ^ { 2 } - 28 x + 35$ 
D)  $x ^ { 4 } - 4 x ^ { 3 } - 12 x ^ { 2 } + 28 x + 35$ 
E) none of these 
A)  $x ^ { 5 } - 4 x ^ { 4 } - 12 x ^ { 3 } + 28 x ^ { 2 } + 35 x - 2$ 
B)  $x ^ { 4 } - 12 x ^ { 2 } + 35$ 
C)  $x ^ { 4 } - 12 x ^ { 3 } - 4 x ^ { 2 } - 28 x + 35$ 
D)  $x ^ { 4 } - 4 x ^ { 3 } - 12 x ^ { 2 } + 28 x + 35$ 
E) none of these

Question 8

Select the graph of the function and determine the zeros of the polynomial. 
 $f ( x ) = x ^ { 2 } ( x - 5 )$

Accepted Answer

A)   $0,5 , - 5$     
B)   $0,5$   
C)   $0 , - 5$   
D)   $0,5$   
E)   $0 , - 5$   
A)   $0,5 , - 5$     
B)   $0,5$   
C)   $0 , - 5$   
D)   $0,5$   
E)   $0 , - 5$

Question 9

Solve the inequality and graph the solution on the real number line.  
  $( x - 7 ) ^ { 2 } \geq 1$

Accepted Answer

A)  $( - \infty , - 6 ] \cup [ - 8 , \infty )$   
B)  $( - \infty , 6 ] \cup [ 8 , \infty )$   
C)  $( - \infty , 8 ] \cup [ 6 , \infty )$   
D)  $( - \infty , 8 ] \cup [ 6 , \infty )$   
E)  $( - \infty , 6 ] \cup [ 8 , \infty )$   
A)  $( - \infty , - 6 ] \cup [ - 8 , \infty )$   
B)  $( - \infty , 6 ] \cup [ 8 , \infty )$   
C)  $( - \infty , 8 ] \cup [ 6 , \infty )$   
D)  $( - \infty , 8 ] \cup [ 6 , \infty )$   
E)  $( - \infty , 6 ] \cup [ 8 , \infty )$

Question 10

Find the interval(s) for b such that the equation has at least one real solution and write a conjecture about the interval(s) based on the values of the coefficients
 $4 x ^ { 2 } + b x + 7 = 0$ .

Accepted Answer

A) $( - \infty , - 2 \sqrt { 28 } ] \cap [ 2 \sqrt { 28 } , \infty )$ If $a > 0$ and $c 0$ , $b \leq - 2 \sqrt { a c }$ or $b \leq 2 \sqrt { a c }$ C) $( - \infty , - 2 \sqrt { 28 } ] \cup [ 2 \sqrt { 28 } , \infty )$ If $a > 0$ and $c > 0$ , $b \leq - 2 \sqrt { a c }$ or $b \geq 2 \sqrt { a c }$ D) $( - \infty , 2 \sqrt { 28 } ] \cup [ 2 \sqrt { 28 } , \infty )$ If $a > 0$ and $c > 0$ , $b \leq 2 \sqrt { a c }$ or $b \geq 2 \sqrt { a c }$ E) $( - \infty , - 2 \sqrt { 28 } ] \cap [ 2 \sqrt { 28 } , \infty )$ If $a < 0$ and $c < 0$ , $b \leq 2 \sqrt { a c }$ or $b \leq 2 \sqrt { a c }$ A) $( - \infty , - 2 \sqrt { 28 } ] \cap [ 2 \sqrt { 28 } , \infty )$ If $a > 0$ and $c 0$ , $b \leq - 2 \sqrt { a c }$ or $b \leq 2 \sqrt { a c }$ C) $( - \infty , - 2 \sqrt { 28 } ] \cup [ 2 \sqrt { 28 } , \infty )$ If $a > 0$ and $c > 0$ , $b \leq - 2 \sqrt { a c }$ or $b \geq 2 \sqrt { a c }$ D) $( - \infty , 2 \sqrt { 28 } ] \cup [ 2 \sqrt { 28 } , \infty )$ If $a > 0$ and $c > 0$ , $b \leq 2 \sqrt { a c }$ or $b \geq 2 \sqrt { a c }$ E) $( - \infty , - 2 \sqrt { 28 } ] \cap [ 2 \sqrt { 28 } , \infty )$ If $a < 0$ and $c < 0$ , $b \leq 2 \sqrt { a c }$ or $b \leq 2 \sqrt { a c }$

Question 11

Using the factors (x - 4) and (x + 2), find the remaining factor(s) of $f ( x ) = x ^ { 3 } + x ^ { 2 } - 14 x - 24$ and write the polynomial in fully factored form.

Accepted Answer

A)  $f ( x ) = ( x - 4 ) ( x + 2 ) ^ { 2 }$ 
B)  $f ( x ) = ( x - 4 ) ( x + 2 ) ( x + 3 )$ 
C)  $f ( x ) = ( x - 4 ) ( x + 2 ) ( x + 7 )$ 
D)  $f ( x ) = ( x - 4 ) ^ { 2 } ( x + 2 )$ 
E)  $f ( x ) = ( x - 4 ) ( x + 2 ) ( x - 3 )$ 
A)  $f ( x ) = ( x - 4 ) ( x + 2 ) ^ { 2 }$ 
B)  $f ( x ) = ( x - 4 ) ( x + 2 ) ( x + 3 )$ 
C)  $f ( x ) = ( x - 4 ) ( x + 2 ) ( x + 7 )$ 
D)  $f ( x ) = ( x - 4 ) ^ { 2 } ( x + 2 )$ 
E)  $f ( x ) = ( x - 4 ) ( x + 2 ) ( x - 3 )$

Question 12

Select from the following which is the polynomial of degree n that has the given zero(s).  
Zeros
Degree $x = 0 , \sqrt { 5 } , - \sqrt { 5 }$ $n = 3$

Accepted Answer

A)  $f ( x ) = x ^ { 3 } + \sqrt { 5 } x$ 
B)  $f ( x ) = x ^ { 3 } + 5 x$ 
C)  $f ( x ) = - x ^ { 3 } - 5 x$ 
D)  $f ( x ) = x ^ { 3 } - \sqrt { 5 } x$ 
E)  $f ( x ) = x ^ { 3 } - 5 x$ 
A)  $f ( x ) = x ^ { 3 } + \sqrt { 5 } x$ 
B)  $f ( x ) = x ^ { 3 } + 5 x$ 
C)  $f ( x ) = - x ^ { 3 } - 5 x$ 
D)  $f ( x ) = x ^ { 3 } - \sqrt { 5 } x$ 
E)  $f ( x ) = x ^ { 3 } - 5 x$

Question 13

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } - 61 x ^ { 2 } + 900$ and determine the multiplicity of each.

Accepted Answer

A)  $x = - 5 , \text { multiplicity } 2 ; x = - 6 , \text { multiplicity } 2$ 
B)  $x = 25 , \text { multiplicity } 2 ; x = 36 \text {, multiplicity } 2$ 
C)  $x = 5 , \text { multiplicity } 2 ; x = 6 , \text { multiplicity } 2$ 
D)  $x = 25 , \text { multiplicity } 2 ; x = 6 , \text { multiplicity } 2$ 
E)  $x = 5 \text {, multiplicity } 1 ; x = - 5 \text {, multiplicity } 1 ; x = 6 \text {, multiplicity } 1 ; x = - 6 \text {, multiplicity } 1$ 
A)  $x = - 5 , \text { multiplicity } 2 ; x = - 6 , \text { multiplicity } 2$ 
B)  $x = 25 , \text { multiplicity } 2 ; x = 36 \text {, multiplicity } 2$ 
C)  $x = 5 , \text { multiplicity } 2 ; x = 6 , \text { multiplicity } 2$ 
D)  $x = 25 , \text { multiplicity } 2 ; x = 6 , \text { multiplicity } 2$ 
E)  $x = 5 \text {, multiplicity } 1 ; x = - 5 \text {, multiplicity } 1 ; x = 6 \text {, multiplicity } 1 ; x = - 6 \text {, multiplicity } 1$

Question 14

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

Accepted Answer

A) x = 0 
B) x = -9 
C) x = 3 
D) x = 9 
E) x = -3 
A) x = 0 
B) x = -9 
C) x = 3 
D) x = 9 
E) x = -3

Question 15

Find all the real zeros of the polynomial function.   $f ( x ) = x ^ { 5 } - 16 x ^ { 3 } + 64 x$

Accepted Answer

A)  $0 , \pm \sqrt { 8 }$ 
B)  $0 , \sqrt { 8 }$ 
C)  $0,8$ 
D)  $0 , - 8$ 
E)  $0 , - \sqrt { 8 }$ 
A)  $0 , \pm \sqrt { 8 }$ 
B)  $0 , \sqrt { 8 }$ 
C)  $0,8$ 
D)  $0 , - 8$ 
E)  $0 , - \sqrt { 8 }$

Question 16

Using a graphing utility, graph $f ( x ) = x ^ { 3 } - 4 x$ and approximate the zeros and their multiplicity.

Accepted Answer

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

Question 17

Find all the real zeros of f(x) = 3x3 - 9x2 + 3x - 9.

Accepted Answer

A) x = 3 
B) x = 3, $- \frac { 1 } { 3 }$ 
C) x = $\frac { 1 } { 3 }$ , $- \frac { 1 } { 9 }$ 
D) x = ±1, 3 
E) x = 3, 1, -9 
A) x = 3 
B) x = 3, $- \frac { 1 } { 3 }$ 
C) x = $\frac { 1 } { 3 }$ , $- \frac { 1 } { 9 }$ 
D) x = ±1, 3 
E) x = 3, 1, -9

Question 18

Select from the following which is the polynomial of degree n that has the given zero(s).  
Zero
Degree $x = 0 , - 3$ $n = 5$

Accepted Answer

A)  $f ( x ) = x ^ { 5 } + 12 x ^ { 4 } + 54 x ^ { 3 } + 108 x ^ { 2 } + 81 x$ 
B)  $f ( x ) = x ^ { 5 } - 12 x ^ { 4 } + 54 x ^ { 3 } + 108 x ^ { 2 } + 81 x$ 
C)  $f ( x ) = x ^ { 5 } + 12 x ^ { 4 } + 54 x ^ { 3 } + 108 x ^ { 2 } - 81 x$ 
D)  $f ( x ) = x ^ { 5 } + 12 x ^ { 4 } - 54 x ^ { 3 } + 108 x ^ { 2 } + 81 x$ 
E)  $f ( x ) = x ^ { 5 } + 12 x ^ { 4 } + 54 x ^ { 3 } - 108 x ^ { 2 } + 81 x$ 
A)  $f ( x ) = x ^ { 5 } + 12 x ^ { 4 } + 54 x ^ { 3 } + 108 x ^ { 2 } + 81 x$ 
B)  $f ( x ) = x ^ { 5 } - 12 x ^ { 4 } + 54 x ^ { 3 } + 108 x ^ { 2 } + 81 x$ 
C)  $f ( x ) = x ^ { 5 } + 12 x ^ { 4 } + 54 x ^ { 3 } + 108 x ^ { 2 } - 81 x$ 
D)  $f ( x ) = x ^ { 5 } + 12 x ^ { 4 } - 54 x ^ { 3 } + 108 x ^ { 2 } + 81 x$ 
E)  $f ( x ) = x ^ { 5 } + 12 x ^ { 4 } + 54 x ^ { 3 } - 108 x ^ { 2 } + 81 x$

Question 19

Use synthetic division to divide. 
$\left( 5 x ^ { 3 } + 27 x ^ { 2 } + 5 x - 25 \right) \div ( x + 5 )$

Accepted Answer

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

Question 20

Find all the zeros of the function and write the polynomial as a product of linear factors. ​
X3 - 6x2 + x + 164
​
​

Accepted Answer

A) -4, 5 ± 4i; (x + 4)(x - 5 + 4i)(x - 5 - 4i) 
B) -4, 5 ± 4i; (x + 4)(x - 5 + 4i)(x + 5 - 4i) 
C) 4, 5 ± 4i; (x - 4)(x - 5 + 4i)(x - 5 - 4i) 
D) -4, 5 ± 4i; (x + 4)(x + 5 + 4i)(x + 5 - 4i) 
E) -4, 5 ± 4i; (x + 4)(x - 5 - 4i)(x - 5 - 4i) 
A) -4, 5 ± 4i; (x + 4)(x - 5 + 4i)(x - 5 - 4i) 
B) -4, 5 ± 4i; (x + 4)(x - 5 + 4i)(x + 5 - 4i) 
C) 4, 5 ± 4i; (x - 4)(x - 5 + 4i)(x - 5 - 4i) 
D) -4, 5 ± 4i; (x + 4)(x + 5 + 4i)(x + 5 - 4i) 
E) -4, 5 ± 4i; (x + 4)(x - 5 - 4i)(x - 5 - 4i)

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

Find the vertex of the parabola. y = - x² + 16x - 60

Use long division to divide. $\left( 6 x ^ { 3 } - 27 x ^ { 2 } + 39 x - 18 \right) \div ( 3 x - 6 )$

Solve the equation and write complex solutions in standard form. $x ^ { 2 } - 18 x + 91 = 0$

The cost C (in millions of dollars) removing p% the industrial and municipal pollutants discharged into a river is given by $C = \frac { 200 p } { 100 - p } , 0 \leq p < 100$ Select the correct graph of the cost function.

Find the zeros (if any) of the rational function. $f ( x ) = 2 + \frac { 12 } { x ^ { 2 } + 2 }$

Find a polynomial with the given zeros. $- 1,5 , - \sqrt { 7 } , \sqrt { 7 }$

Select the graph of the function and determine the zeros of the polynomial. $f ( x ) = x ^ { 2 } ( x - 5 )$

Solve the inequality and graph the solution on the real number line. $( x - 7 ) ^ { 2 } \geq 1$

Find the interval(s) for b such that the equation has at least one real solution and write a conjecture about the interval(s) based on the values of the coefficients $4 x ^ { 2 } + b x + 7 = 0$ .

Using the factors (x - 4) and (x + 2), find the remaining factor(s) of $f ( x ) = x ^ { 3 } + x ^ { 2 } - 14 x - 24$ and write the polynomial in fully factored form.

Select from the following which is the polynomial of degree n that has the given zero(s). Zeros Degree $x = 0 , \sqrt { 5 } , - \sqrt { 5 }$ $n = 3$

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } - 61 x ^ { 2 } + 900$ and determine the multiplicity of each.

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

Find all the real zeros of the polynomial function. $f ( x ) = x ^ { 5 } - 16 x ^ { 3 } + 64 x$

Using a graphing utility, graph $f ( x ) = x ^ { 3 } - 4 x$ and approximate the zeros and their multiplicity.

Find all the real zeros of f(x) = 3x³ - 9x² + 3x - 9.

Select from the following which is the polynomial of degree n that has the given zero(s). Zero Degree $x = 0 , - 3$ $n = 5$

Use synthetic division to divide. $\left( 5 x ^ { 3 } + 27 x ^ { 2 } + 5 x - 25 \right) \div ( x + 5 )$

Find all the zeros of the function and write the polynomial as a product of linear factors. X³ - 6x² + x + 164

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

Determine the equations of the vertical and horizontal asymptotes of the graph of the function f(x)=xx−4f ( x ) = \frac { x } { x - 4 }f(x)=x−4x​ .

Find the vertex of the parabola. y = - x2 + 16x - 60

Use long division to divide. (6x3−27x2+39x−18)÷(3x−6)\left( 6 x ^ { 3 } - 27 x ^ { 2 } + 39 x - 18 \right) \div ( 3 x - 6 )(6x3−27x2+39x−18)÷(3x−6)

Solve the equation and write complex solutions in standard form. x2−18x+91=0x ^ { 2 } - 18 x + 91 = 0x2−18x+91=0

The cost C (in millions of dollars) removing p% the industrial and municipal pollutants discharged into a river is given by C=200p100−p,0≤p<100C = \frac { 200 p } { 100 - p } , 0 \leq p < 100C=100−p200p​,0≤p<100 Select the correct graph of the cost function.

Find the zeros (if any) of the rational function. f(x)=2+12x2+2f ( x ) = 2 + \frac { 12 } { x ^ { 2 } + 2 }f(x)=2+x2+212​

Find a polynomial with the given zeros. −1,5,−7,7- 1,5 , - \sqrt { 7 } , \sqrt { 7 }−1,5,−7​,7​

Select the graph of the function and determine the zeros of the polynomial. f(x)=x2(x−5)f ( x ) = x ^ { 2 } ( x - 5 )f(x)=x2(x−5)

Solve the inequality and graph the solution on the real number line. (x−7)2≥1( x - 7 ) ^ { 2 } \geq 1(x−7)2≥1

Find the interval(s) for b such that the equation has at least one real solution and write a conjecture about the interval(s) based on the values of the coefficients 4x2+bx+7=04 x ^ { 2 } + b x + 7 = 04x2+bx+7=0 .

Using the factors (x - 4) and (x + 2), find the remaining factor(s) of f(x)=x3+x2−14x−24f ( x ) = x ^ { 3 } + x ^ { 2 } - 14 x - 24f(x)=x3+x2−14x−24 and write the polynomial in fully factored form.

Select from the following which is the polynomial of degree n that has the given zero(s). Zeros Degree x=0,5,−5x = 0 , \sqrt { 5 } , - \sqrt { 5 }x=0,5​,−5​ n=3n = 3n=3

Find all real zeros of the polynomial f(x)=x4−61x2+900f ( x ) = x ^ { 4 } - 61 x ^ { 2 } + 900f(x)=x4−61x2+900 and determine the multiplicity of each.

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

Find all the real zeros of the polynomial function. f(x)=x5−16x3+64xf ( x ) = x ^ { 5 } - 16 x ^ { 3 } + 64 xf(x)=x5−16x3+64x

Using a graphing utility, graph f(x)=x3−4xf ( x ) = x ^ { 3 } - 4 xf(x)=x3−4x and approximate the zeros and their multiplicity.

Find all the real zeros of f(x) = 3x3 - 9x2 + 3x - 9.

Select from the following which is the polynomial of degree n that has the given zero(s). Zero Degree x=0,−3x = 0 , - 3x=0,−3 n=5n = 5n=5

Use synthetic division to divide. (5x3+27x2+5x−25)÷(x+5)\left( 5 x ^ { 3 } + 27 x ^ { 2 } + 5 x - 25 \right) \div ( x + 5 )(5x3+27x2+5x−25)÷(x+5)

Find all the zeros of the function and write the polynomial as a product of linear factors. ​ X3 - 6x2 + x + 164 ​ ​

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

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

Find the vertex of the parabola. y = - x² + 16x - 60

Use long division to divide. $\left( 6 x ^ { 3 } - 27 x ^ { 2 } + 39 x - 18 \right) \div ( 3 x - 6 )$

Solve the equation and write complex solutions in standard form. $x ^ { 2 } - 18 x + 91 = 0$

The cost C (in millions of dollars) removing p% the industrial and municipal pollutants discharged into a river is given by $C = \frac { 200 p } { 100 - p } , 0 \leq p < 100$ Select the correct graph of the cost function.

Find the zeros (if any) of the rational function. $f ( x ) = 2 + \frac { 12 } { x ^ { 2 } + 2 }$

Find a polynomial with the given zeros. $- 1,5 , - \sqrt { 7 } , \sqrt { 7 }$

Select the graph of the function and determine the zeros of the polynomial. $f ( x ) = x ^ { 2 } ( x - 5 )$

Solve the inequality and graph the solution on the real number line. $( x - 7 ) ^ { 2 } \geq 1$

Find the interval(s) for b such that the equation has at least one real solution and write a conjecture about the interval(s) based on the values of the coefficients $4 x ^ { 2 } + b x + 7 = 0$ .

Using the factors (x - 4) and (x + 2), find the remaining factor(s) of $f ( x ) = x ^ { 3 } + x ^ { 2 } - 14 x - 24$ and write the polynomial in fully factored form.

Select from the following which is the polynomial of degree n that has the given zero(s). Zeros Degree $x = 0 , \sqrt { 5 } , - \sqrt { 5 }$ $n = 3$

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } - 61 x ^ { 2 } + 900$ and determine the multiplicity of each.

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

Find all the real zeros of the polynomial function. $f ( x ) = x ^ { 5 } - 16 x ^ { 3 } + 64 x$

Using a graphing utility, graph $f ( x ) = x ^ { 3 } - 4 x$ and approximate the zeros and their multiplicity.

Find all the real zeros of f(x) = 3x³ - 9x² + 3x - 9.

Select from the following which is the polynomial of degree n that has the given zero(s). Zero Degree $x = 0 , - 3$ $n = 5$

Use synthetic division to divide. $\left( 5 x ^ { 3 } + 27 x ^ { 2 } + 5 x - 25 \right) \div ( x + 5 )$

Find all the zeros of the function and write the polynomial as a product of linear factors. X³ - 6x² + x + 164