Question 1

Find the zeros of the polynomial function below. If a zero is a multiple zero, state its multiplicity.

Accepted Answer

A) 3, 4 (multiplicity 2) 
B) -3, 4 (multiplicity 2) 
C) 3, -4 (multiplicity 2) 
D) -4, -3 (multiplicity 2) 
E) 4, 3 (multiplicity 2) 
A) 3, 4 (multiplicity 2) 
B) -3, 4 (multiplicity 2) 
C) 3, -4 (multiplicity 2) 
D) -4, -3 (multiplicity 2) 
E) 4, 3 (multiplicity 2)

Question 2

Find the real zeros of the polynomial function below by factoring.

Accepted Answer

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

Question 3

Find a polynomial function P of degree 5 with integer coefficients that has zeros   ,   (multiplicity 2),   , and   .

Accepted Answer

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

Question 4

Find a polynomial function of lowest degree with integer coefficients, whose leading coefficient is one, and that has the zeros 8,   , and 3 i .

Accepted Answer

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

Question 5

Find the zeros of the polynomial function below. If a zero is a multiple zero, state its multiplicity.

Accepted Answer

A) 1,   ,   
B)    ,   ,   
C)    ,   ,   
D)    ,   ,   
E) 1,   ,   
A) 1,   ,   
B)    ,   ,   
C)    ,   ,   
D)    ,   ,   
E) 1,   ,

Question 6

Sketch the graph of the rational function   .

Accepted Answer

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

Question 7

Find the slant asymptote of the rational function   .

Accepted Answer

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

Question 8

A closed box is to be constructed from a rectangular sheet of cardboard that measures 21 inches by 10 inches. The box is made by cutting rectangles that measure x inches by 2 x 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) 1.918 
B) 7.709 
C) 1.352 
D) 1.513 
E) 6.082 
A) 1.918 
B) 7.709 
C) 1.352 
D) 1.513 
E) 6.082

Question 9

Use the Remainder Theorem to find P( 8)for   .

Accepted Answer

A) 4,368 
B) -4,352 
C) -4,864 
D) 374,288 
E) 4880 
A) 4,368 
B) -4,352 
C) -4,864 
D) 374,288 
E) 4880

Question 10

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 11

A software company produces a computer game. The company has determined that its profit P , in dollars, from the manufacture and sale of x games is given by   where   . How many games, to the nearest unit, does the company need to produce and sell to obtain the maximum profit?

Accepted Answer

A) 5711 games 
B) 5756 games 
C) 5716 games 
D) 5706 games 
E) 5701 games 
A) 5711 games 
B) 5756 games 
C) 5716 games 
D) 5706 games 
E) 5701 games

Question 12

Determine the x -intercepts of the graph of the polynomial below. For each x -intercept, use the Even and Odd Powers of   Theorem to determine whether the graph of the polynomial crosses the x -axis or intersects but does not cross the x -axis.

Accepted Answer

A) crosses the x -axis at   ,   , and   
B) crosses the x -axis at   ; intersects the x -axis at   and   
C) crosses the x -axis at   and   ; intersects the x -axis at   
D) crosses the x -axis at   and   ; intersects the x -axis at   
E) crosses the x -axis at   and   ; intersects the x -axis at   
A) crosses the x -axis at   ,   , and   
B) crosses the x -axis at   ; intersects the x -axis at   and   
C) crosses the x -axis at   and   ; intersects the x -axis at   
D) crosses the x -axis at   and   ; intersects the x -axis at   
E) crosses the x -axis at   and   ; intersects the x -axis at

Question 13

Determine the vertical and slant asymptotes of the rational function below.

Accepted Answer

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

Question 14

Use a graph and your knowledge of the zeros of polynomial functions to determine the exact values of all the solutions of the equation below.

Accepted Answer

A)    (multiplicity 2) 
B)    (multiplicity 2) 
C)    (multiplicity 2) 
D)    (multiplicity 2) 
E)    (multiplicity 2) 
A)    (multiplicity 2) 
B)    (multiplicity 2) 
C)    (multiplicity 2) 
D)    (multiplicity 2) 
E)    (multiplicity 2)

Question 15

Use Descartes Rule of Signs to determine the number of possible positive real zeros and the number of possible negative real zeros of   .

Accepted Answer

A) positive zeros: 2 or 0 negative zeros: 3 or 1 
B) positive zeros: 1 negative zeros: 2 or 0 
C) positive zeros: 3 or 1 negative zeros: 2 or 0 
D) positive zeros: 2 negative zeros: 1 
E) positive zeros: 2 or 0 negative zeros: 1 
A) positive zeros: 2 or 0 negative zeros: 3 or 1 
B) positive zeros: 1 negative zeros: 2 or 0 
C) positive zeros: 3 or 1 negative zeros: 2 or 0 
D) positive zeros: 2 negative zeros: 1 
E) positive zeros: 2 or 0 negative zeros: 1

Question 16

Graph the polynomial   . Estimate, to the nearest tenth, the coordinates of the points where   has a relative maximum or a relative minimum. For each point, indicate whether the y value is a relative maximum or a relative minimum.

Accepted Answer

A)    has a relative maximum of 6.0 at   and a relative minimum of   at   . 
B)    has a relative maximum of 6.0 at   and a relative minimum of   at   . 
C)    has a relative maximum of 6.0 at   and a relative minimum of 108.0 at   . 
D)    has a relative maximum of 6.0 at   and a relative minimum of   at   . 
E)    has a relative maximum of 6.0 at   and a relative minimum of   at   . 
A)    has a relative maximum of 6.0 at   and a relative minimum of   at   . 
B)    has a relative maximum of 6.0 at   and a relative minimum of   at   . 
C)    has a relative maximum of 6.0 at   and a relative minimum of 108.0 at   . 
D)    has a relative maximum of 6.0 at   and a relative minimum of   at   . 
E)    has a relative maximum of 6.0 at   and a relative minimum of   at   .

Question 17

Find the smallest positive integer and the largest negative integer that, by the Upper- and Lower-Bound Theorem, are upper and lower bounds, respectively, for the real zeros of the polynomial function   .

Accepted Answer

A) upper bound 3, lower bound -4 
B) upper bound 20, lower bound -28 
C) upper bound 28, lower bound -28 
D) upper bound 4, lower bound -1 
E) upper bound 20, lower bound -20 
A) upper bound 3, lower bound -4 
B) upper bound 20, lower bound -28 
C) upper bound 28, lower bound -28 
D) upper bound 4, lower bound -1 
E) upper bound 20, lower bound -20

Question 18

The cost, in dollars, of producing x cellular telephones is given by   . The average cost per telephone is   . Find the average cost per telephone, rounded to the nearest cent, when   telephones are produced.

Accepted Answer

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

Question 19

Determine the vertical and slant asymptotes of the rational function below.

Accepted Answer

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

Question 20

Given   is a zero of the polynomial function   , find the remaining zeros of the polynomial.

Accepted Answer

A)    
B)    
C)    
D) 2, -1 + 5 i 
E)    
A)    
B)    
C)    
D) 2, -1 + 5 i 
E)

Find the zeros of the polynomial function below. If a zero is a multiple zero, state its multiplicity.

Find the real zeros of the polynomial function below by factoring.

Find a polynomial function P of degree 5 with integer coefficients that has zeros , (multiplicity 2), , and .

Find a polynomial function of lowest degree with integer coefficients, whose leading coefficient is one, and that has the zeros 8, , and 3 i .

Find the zeros of the polynomial function below. If a zero is a multiple zero, state its multiplicity.

Sketch the graph of the rational function .

Find the slant asymptote of the rational function .

Use the Remainder Theorem to find P( 8)for .

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

A software company produces a computer game. The company has determined that its profit P , in dollars, from the manufacture and sale of x games is given by where . How many games, to the nearest unit, does the company need to produce and sell to obtain the maximum profit?

Determine the x -intercepts of the graph of the polynomial below. For each x -intercept, use the Even and Odd Powers of Theorem to determine whether the graph of the polynomial crosses the x -axis or intersects but does not cross the x -axis.

Determine the vertical and slant asymptotes of the rational function below.

Use a graph and your knowledge of the zeros of polynomial functions to determine the exact values of all the solutions of the equation below.

Use Descartes Rule of Signs to determine the number of possible positive real zeros and the number of possible negative real zeros of .

Graph the polynomial . Estimate, to the nearest tenth, the coordinates of the points where has a relative maximum or a relative minimum. For each point, indicate whether the y value is a relative maximum or a relative minimum.

Find the smallest positive integer and the largest negative integer that, by the Upper- and Lower-Bound Theorem, are upper and lower bounds, respectively, for the real zeros of the polynomial function .

The cost, in dollars, of producing x cellular telephones is given by . The average cost per telephone is . Find the average cost per telephone, rounded to the nearest cent, when telephones are produced.

Determine the vertical and slant asymptotes of the rational function below.

Given is a zero of the polynomial function , find the remaining zeros of the polynomial.

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Exam 3: Polynomial and Rational Functions

Find the zeros of the polynomial function below. If a zero is a multiple zero, state its multiplicity.

Find the real zeros of the polynomial function below by factoring.

Find a polynomial function P of degree 5 with integer coefficients that has zeros , (multiplicity 2), , and .

Find a polynomial function of lowest degree with integer coefficients, whose leading coefficient is one, and that has the zeros 8, , and 3 i .

Find the zeros of the polynomial function below. If a zero is a multiple zero, state its multiplicity.

Sketch the graph of the rational function .

Find the slant asymptote of the rational function .

Use the Remainder Theorem to find P( 8)for .

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

A software company produces a computer game. The company has determined that its profit P , in dollars, from the manufacture and sale of x games is given by where . How many games, to the nearest unit, does the company need to produce and sell to obtain the maximum profit?

Determine the x -intercepts of the graph of the polynomial below. For each x -intercept, use the Even and Odd Powers of Theorem to determine whether the graph of the polynomial crosses the x -axis or intersects but does not cross the x -axis.

Determine the vertical and slant asymptotes of the rational function below.

Use a graph and your knowledge of the zeros of polynomial functions to determine the exact values of all the solutions of the equation below.

Use Descartes Rule of Signs to determine the number of possible positive real zeros and the number of possible negative real zeros of .

Graph the polynomial . Estimate, to the nearest tenth, the coordinates of the points where has a relative maximum or a relative minimum. For each point, indicate whether the y value is a relative maximum or a relative minimum.

Find the smallest positive integer and the largest negative integer that, by the Upper- and Lower-Bound Theorem, are upper and lower bounds, respectively, for the real zeros of the polynomial function .

The cost, in dollars, of producing x cellular telephones is given by . The average cost per telephone is . Find the average cost per telephone, rounded to the nearest cent, when telephones are produced.

Determine the vertical and slant asymptotes of the rational function below.

Given is a zero of the polynomial function , find the remaining zeros of the polynomial.

Equations and Inequalities

Functions and Graphs

Exponential and Logarithmic Functions

Trigonometric Functions

Trigonometric Identities and Equations

Applications of Trigonometry

Topics in Analytic Geometry

Systems of Equations and Inequalities

Matrices

Sequences, Series, and Probability

Preliminary Concepts

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