Question 1

Find a polynomial with the given zeros.​ $7,1$ ​

Accepted Answer

A)  $x ^ { 2 } - 8 x + 7$ 
B)  $x ^ { 2 } - 8 x + 8$ 
C)  $x ^ { 2 } - 8 x - 7$ 
D)  $8 x ^ { 2 } - x + 7$ 
E) none of these 
A)  $x ^ { 2 } - 8 x + 7$ 
B)  $x ^ { 2 } - 8 x + 8$ 
C)  $x ^ { 2 } - 8 x - 7$ 
D)  $8 x ^ { 2 } - x + 7$ 
E) none of these

Question 2

Select from the following which is the polynomial function that has the given zeros.​ $1 + \sqrt { 5 } , 1 - \sqrt { 5 }$ ​

Accepted Answer

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

Question 3

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 4

Describe the right-hand and the left-hand behavior of the graph of $q ( x ) = - \frac { 7 } { 12 } \left( x ^ { 3 } - x ^ { 2 } + 2 x + 1 \right)$ .

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 negative,the graph falls to the left and rises to the right. 
C) Because the degree is odd and the leading coefficient is positive,the graph falls to the left and falls 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 negative,the graph rises to the left and falls to the right. 
B) Because the degree is odd and the leading coefficient is negative,the graph falls to the left and rises to the right. 
C) Because the degree is odd and the leading coefficient is positive,the graph falls to the left and falls 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 5

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 6

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 7

Find all real zeros of the polynomial $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 36 x - 108$ and determine the multiplicity of each.

Accepted Answer

A)  $x = 6 , \text { multiplicity } 2 ; x = - 3 \text {, multiplicity } 1$ 
B)  $x = 6 \text {, multiplicity } 1 ; x = - 6 \text {, multiplicity } 1 ; x = - 3 \text {, multiplicity } 1$ 
C)  $x = - 3 \text {, multiplicity } 2 ; x = - 6 \text {, multiplicity } 1$ 
D)  $x = - 6 \text {, multiplicity } 1 ; x = 3 \text {, multiplicity } 1 ; x = - 3 \text {, multiplicity } 1$ 
E)  $x = - 3 \text {, multiplicity } 3$ 
A)  $x = 6 , \text { multiplicity } 2 ; x = - 3 \text {, multiplicity } 1$ 
B)  $x = 6 \text {, multiplicity } 1 ; x = - 6 \text {, multiplicity } 1 ; x = - 3 \text {, multiplicity } 1$ 
C)  $x = - 3 \text {, multiplicity } 2 ; x = - 6 \text {, multiplicity } 1$ 
D)  $x = - 6 \text {, multiplicity } 1 ; x = 3 \text {, multiplicity } 1 ; x = - 3 \text {, multiplicity } 1$ 
E)  $x = - 3 \text {, multiplicity } 3$

Question 8

Find all real zeros of the polynomial $$f ( x ) = x ^ { 4 } + 7 x ^ { 3 } + 6 x ^ { 2 }$$ and determine the multiplicity of each.

Accepted Answer

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

Question 9

Well whether the function $y = x ^ { 5 } + 9 x ^ { 3 }$ is even or odd.If it is neither,so indicate. ​

Accepted Answer

A) even 
B) odd 
C) neither 
A) even 
B) odd 
C) neither

Question 10

Select the graph of the function and determine the zeros of the polynomial.​ $$f ( x ) = x ^ { 3 } - 5 x ^ { 2 }$$ ​

Accepted Answer

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

Question 11

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 12

An open box is to be made from a square piece of cardboard,28 inches on a side,by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below).Determine the function,V,in terms of x,that represents the volume of the box.

Accepted Answer

A)  $V ( x ) = - 2 x ^ { 3 } + 28 x ^ { 2 }$ 
B)  $V ( x ) = - 4 x ^ { 3 } + 56 x ^ { 2 }$ 
C)  $V ( x ) = 4 x ^ { 3 } - 56 x ^ { 2 } + 28 x$ 
D)  $V ( x ) = - 4 x ^ { 3 } + 56 x ^ { 2 } - 28 x$ 
E)  $V ( x ) = 4 x ^ { 3 } - 112 x ^ { 2 } + 784 x$ 
A)  $V ( x ) = - 2 x ^ { 3 } + 28 x ^ { 2 }$ 
B)  $V ( x ) = - 4 x ^ { 3 } + 56 x ^ { 2 }$ 
C)  $V ( x ) = 4 x ^ { 3 } - 56 x ^ { 2 } + 28 x$ 
D)  $V ( x ) = - 4 x ^ { 3 } + 56 x ^ { 2 } - 28 x$ 
E)  $V ( x ) = 4 x ^ { 3 } - 112 x ^ { 2 } + 784 x$

Question 13

Graph the polynomial function.​ $$y = x ^ { 3 } + 5 x ^ { 2 }$$ ​

Accepted Answer

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

Question 14

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 15

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

Accepted Answer

A)  $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 27 x - 27$ 
B)  $f ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 27 x - 27$ 
C)  $f ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 27 x + 27$ 
D)  $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 27 x + 27$ 
E)  $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } - 27 x - 27$ 
A)  $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 27 x - 27$ 
B)  $f ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 27 x - 27$ 
C)  $f ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 27 x + 27$ 
D)  $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 27 x + 27$ 
E)  $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } - 27 x - 27$

Question 16

Select from the following which is the polynomial function that has the given zeros.​ $$0 , - 7 , - 3$$ ​

Accepted Answer

A)  $f ( x ) = - x ^ { 3 } + 10 x ^ { 2 } + 21 x$ 
B)  $f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 21 x$ 
C)  $f ( x ) = x ^ { 3 } + 10 x ^ { 2 } + 21 x$ 
D)  $f ( x ) = x ^ { 3 } - 10 x ^ { 2 } - 21 x$ 
E)  $f ( x ) = x ^ { 3 } + 10 x ^ { 2 } - 21 x$ 
A)  $f ( x ) = - x ^ { 3 } + 10 x ^ { 2 } + 21 x$ 
B)  $f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 21 x$ 
C)  $f ( x ) = x ^ { 3 } + 10 x ^ { 2 } + 21 x$ 
D)  $f ( x ) = x ^ { 3 } - 10 x ^ { 2 } - 21 x$ 
E)  $f ( x ) = x ^ { 3 } + 10 x ^ { 2 } - 21 x$

Question 17

Select the correct description of right-hand and left-hand behavior of the graph of the polynomial function.​ $$f ( x ) = 2 x ^ { 2 } - 3 x + 5$$ ​

Accepted Answer

A) Falls to the left,rises to the right 
B) Falls to the left,falls to the right 
C) Rises to the left,rises to the right 
D) Rises to the left,falls to the right 
E) Falls to the left 
A) Falls to the left,rises to the right 
B) Falls to the left,falls to the right 
C) Rises to the left,rises to the right 
D) Rises to the left,falls to the right 
E) Falls to the left

Question 18

Select the graph of the function and determine the zeros of the polynomial.​ $$g ( t ) = - \frac { 1 } { 4 } ( t - 2 ) ^ { 2 } ( t + 2 ) ^ { 2 }$$ ​

Accepted Answer

A) ​ $$- 2$$   ​ 
B) ​ $$2$$   ​ 
C) ​ $$\pm 2$$   ​ 
D) ​ $$2$$   ​ 
E) ​ $$- 2$$   ​ 
A) ​ $$- 2$$   ​ 
B) ​ $$2$$   ​ 
C) ​ $$\pm 2$$   ​ 
D) ​ $$2$$   ​ 
E) ​ $$- 2$$   ​

Question 19

An open box is to be made from a square piece of cardboard,22 inches on a side,by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below).If the volume of the box is represented by $V ( x ) = x ( 22 - 2 x ) ^ { 2 }$ ,determine the domain of $V ( x )$ .

Accepted Answer

A)  $D = \{ x \mid 0  0 \}$ 
D)  $D = \{ x \mid 44 < x < 88 \}$ 
E)  $D = \{ x \mid 11 < x < 22 \}$ 
A)  $D = \{ x \mid 0  0 \}$ 
D)  $D = \{ x \mid 44 < x < 88 \}$ 
E)  $D = \{ x \mid 11 < x < 22 \}$

Question 20

Sketch the graph of the function by finding the zeros of the polynomial,​ $$f ( x ) = 2 x ^ { 3 } - 10 x ^ { 2 } + 12 x$$ ​

Accepted Answer

A) ​ ​0,2,3  
​ 
B) ​ ​0,2,-3  
​ 
C) ​ ​0,-2,3  
​ 
D) ​ ​0,2,3  
​ 
E) ​ ​0,-2,-3  
​ 
A) ​ ​0,2,3  
​ 
B) ​ ​0,2,-3  
​ 
C) ​ ​0,-2,3  
​ 
D) ​ ​0,2,3  
​ 
E) ​ ​0,-2,-3  
​

Exam 12: Polynomial Functions of Higher Degree

Find a polynomial with the given zeros.​ 7,17,17,1 ​

Select from the following which is the polynomial function that has the given zeros.​ 1+5,1−51 + \sqrt { 5 } , 1 - \sqrt { 5 }1+5​,1−5​ ​

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 ​

Describe the right-hand and the left-hand behavior of the graph of q(x)=−712(x3−x2+2x+1)q ( x ) = - \frac { 7 } { 12 } \left( x ^ { 3 } - x ^ { 2 } + 2 x + 1 \right)q(x)=−127​(x3−x2+2x+1) .

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.

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 ​ ​

Find all real zeros of the polynomial f(x)=x3+3x2−36x−108f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 36 x - 108f(x)=x3+3x2−36x−108 and determine the multiplicity of each.

Find all real zeros of the polynomial f(x)=x4+7x3+6x2f ( x ) = x ^ { 4 } + 7 x ^ { 3 } + 6 x ^ { 2 }f(x)=x4+7x3+6x2 and determine the multiplicity of each.

Well whether the function y=x5+9x3y = x ^ { 5 } + 9 x ^ { 3 }y=x5+9x3 is even or odd.If it is neither,so indicate. ​

Select the graph of the function and determine the zeros of the polynomial.​ f(x)=x3−5x2f ( x ) = x ^ { 3 } - 5 x ^ { 2 }f(x)=x3−5x2 ​

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.

An open box is to be made from a square piece of cardboard,28 inches on a side,by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below).Determine the function,V,in terms of x,that represents the volume of the box.

Graph the polynomial function.​ y=x3+5x2y = x ^ { 3 } + 5 x ^ { 2 }y=x3+5x2 ​

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 ​ ​

Select from the following which is the polynomial of degree n that has the given zero(s). ​ Zero Degree x=3x = 3x=3 n=3n = 3n=3 ​ ​

Select from the following which is the polynomial function that has the given zeros.​ 0,−7,−30 , - 7 , - 30,−7,−3 ​

Select the correct description of right-hand and left-hand behavior of the graph of the polynomial function.​ f(x)=2x2−3x+5f ( x ) = 2 x ^ { 2 } - 3 x + 5f(x)=2x2−3x+5 ​

Select the graph of the function and determine the zeros of the polynomial.​ g(t)=−14(t−2)2(t+2)2g ( t ) = - \frac { 1 } { 4 } ( t - 2 ) ^ { 2 } ( t + 2 ) ^ { 2 }g(t)=−41​(t−2)2(t+2)2 ​

Sketch the graph of the function by finding the zeros of the polynomial,​ f(x)=2x3−10x2+12xf ( x ) = 2 x ^ { 3 } - 10 x ^ { 2 } + 12 xf(x)=2x3−10x2+12x ​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Find a polynomial with the given zeros. $7,1$

Select from the following which is the polynomial function that has the given zeros. $1 + \sqrt { 5 } , 1 - \sqrt { 5 }$

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

Describe the right-hand and the left-hand behavior of the graph of $q ( x ) = - \frac { 7 } { 12 } \left( x ^ { 3 } - x ^ { 2 } + 2 x + 1 \right)$ .

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

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

Find all real zeros of the polynomial $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 36 x - 108$ and determine the multiplicity of each.

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 7 x ^ { 3 } + 6 x ^ { 2 }$ and determine the multiplicity of each.

Well whether the function $y = x ^ { 5 } + 9 x ^ { 3 }$ is even or odd.If it is neither,so indicate.

Select the graph of the function and determine the zeros of the polynomial. $f ( x ) = x ^ { 3 } - 5 x ^ { 2 }$

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

Graph the polynomial function. $y = x ^ { 3 } + 5 x ^ { 2 }$

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

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

Select from the following which is the polynomial function that has the given zeros. $0 , - 7 , - 3$

Select the correct description of right-hand and left-hand behavior of the graph of the polynomial function. $f ( x ) = 2 x ^ { 2 } - 3 x + 5$

Select the graph of the function and determine the zeros of the polynomial. $g ( t ) = - \frac { 1 } { 4 } ( t - 2 ) ^ { 2 } ( t + 2 ) ^ { 2 }$

Sketch the graph of the function by finding the zeros of the polynomial, $f ( x ) = 2 x ^ { 3 } - 10 x ^ { 2 } + 12 x$