Question 1

Use the zero   of   to find all the zeros of f.

Accepted Answer

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

Question 2

Use long division to divide.

Accepted Answer

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

Question 3

A closed box is to be constructed from a rectangular sheet of cardboard that measures 57 inches by 28 inches.The box is made by cutting rectangles that measure x inches by 2x inches from two of the corners and by cutting two squares that measure x inches by x inches from the top and from the bottom of the rectangle, as shown in the following figure.Use a graphing calculator to determine what value of x (to the nearest thousandth of an inch) will produce a box with maximum volume?

Accepted Answer

A)  5.314 
B)  21.000 
C)  4.222 
D)  16.686 
E)  3.707 
A)  5.314 
B)  21.000 
C)  4.222 
D)  16.686 
E)  3.707

Question 4

The graph of the function   is shown below.Determine the vertical and horizontal asymptotes of its graph.

Accepted Answer

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

Question 5

Using the factors   and   , find the remaining factor(s) of   and write the polynomial in fully factored form.

Accepted Answer

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

Question 6

Simplify   and write the answer in standard form.

Accepted Answer

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

Question 7

Find all the rational zeros of the function

Accepted Answer

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

Question 8

Write the complex number   in standard form.

Accepted Answer

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

Question 9

Use synthetic division and the Factor Theorem to determine whether or not   is a factor of

Accepted Answer

A)  Yes,   is a factor. 
B)  No,   is not a factor. 
A)  Yes,   is a factor. 
B)  No,   is not a factor.

Question 10

Use the zero   of   to find all the zeros of f.

Accepted Answer

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

Question 11

Describe the right-hand and the left-hand behavior of the graph of

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 12

Use synthetic division and the Factor Theorem to determine whether or not   is a factor of

Accepted Answer

A)  No,   is not a factor. 
B)  Yes,   is a factor. 
A)  No,   is not a factor. 
B)  Yes,   is a factor.

Question 13

If   , use synthetic division to evaluate

Accepted Answer

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

Question 14

Use long division to divide.

Accepted Answer

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

Question 15

Write the polynomial   as the product of linear and quadratic factors that are irreducible over the reals.

Accepted Answer

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

Question 16

Simplify and write the following complex number in standard form.

Accepted Answer

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

Question 17

Use long division to divide the first polynomial below by the second.

Accepted Answer

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

Question 18

Use the zero or root feature of a graphing utility to approximate the real zeros of the function   accurate to the nearest thousandth.

Accepted Answer

A)    , 1.732, 1.414 
B)  -1.732, -1.414 
C)    1.732,   1.414 
D)  1.732, 1.414 
E)    , - 1.732, 1.414 
A)    , 1.732, 1.414 
B)  -1.732, -1.414 
C)    1.732,   1.414 
D)  1.732, 1.414 
E)    , - 1.732, 1.414

Question 19

Use synthetic division to divide.

Accepted Answer

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

Question 20

Given   , determine the equations of any slant and vertical asymptote.

Accepted Answer

A)  slant:   ; vertical:   
B)  slant:   ; vertical:   
C)  slant:   ; vertical:   
D)  slant:   ; vertical:   
E)  slant:   ; vertical: none 
A)  slant:   ; vertical:   
B)  slant:   ; vertical:   
C)  slant:   ; vertical:   
D)  slant:   ; vertical:   
E)  slant:   ; vertical: none

Use the zero of to find all the zeros of f.

Use long division to divide.

The graph of the function is shown below.Determine the vertical and horizontal asymptotes of its graph.

Using the factors and , find the remaining factor(s) of and write the polynomial in fully factored form.

Simplify and write the answer in standard form.

Find all the rational zeros of the function

Write the complex number in standard form.

Use synthetic division and the Factor Theorem to determine whether or not is a factor of

Use the zero of to find all the zeros of f.

Describe the right-hand and the left-hand behavior of the graph of

Use synthetic division and the Factor Theorem to determine whether or not is a factor of

If , use synthetic division to evaluate

Use long division to divide.

Write the polynomial as the product of linear and quadratic factors that are irreducible over the reals.

Simplify and write the following complex number in standard form.

Use long division to divide the first polynomial below by the second.

Use the zero or root feature of a graphing utility to approximate the real zeros of the function accurate to the nearest thousandth.

Use synthetic division to divide.

Given , determine the equations of any slant and vertical asymptote.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants

Sequences, Series, and Probability

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Exam 3: Polynomial and Rational Functions

Use the zero of to find all the zeros of f.

Use long division to divide.

The graph of the function is shown below.Determine the vertical and horizontal asymptotes of its graph.

Using the factors and , find the remaining factor(s) of and write the polynomial in fully factored form.

Simplify and write the answer in standard form.

Find all the rational zeros of the function

Write the complex number in standard form.

Use synthetic division and the Factor Theorem to determine whether or not is a factor of

Use the zero of to find all the zeros of f.

Describe the right-hand and the left-hand behavior of the graph of

Use synthetic division and the Factor Theorem to determine whether or not is a factor of

If , use synthetic division to evaluate

Use long division to divide.

Write the polynomial as the product of linear and quadratic factors that are irreducible over the reals.

Simplify and write the following complex number in standard form.

Use long division to divide the first polynomial below by the second.

Use the zero or root feature of a graphing utility to approximate the real zeros of the function accurate to the nearest thousandth.

Use synthetic division to divide.

Given , determine the equations of any slant and vertical asymptote.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants

Sequences, Series, and Probability

Filters