Deck 3: Polynomial and Rational Functions

Question 1

Find an equation of the parabola that has a vertex at and whose graph passes through the point

A)
B)
C)
D)
E)

Answer 1

B

Question 2

Find all real zeros of the polynomial and determine the mutiplicity of each.

A) , multiplicity 2; , multiplicity 2
B) , multiplicity 2; , multiplicity 2
C) , multiplicity 2; , multiplicity 1
D) , multiplicity 2; , multiplicity 2
E) , multiplicity 1; , multiplicity 1; , multiplicity 1; , multiplicity 1

Answer 2

E

Question 3

Match the equation with its graph.

A)
B)
C)
D)
E)

Answer 3

E

Question 4

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

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 5

Determine the vertex of the graph of the quadratic function

A)
B)
C)
D)
E)

Question 6

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

A) Because the degree is even and the leading coefficient is negative, the graph falls to the left and falls to the right.
B) Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right.
C) Because the degree is even and the leading coefficient is negative, the graph falls to the left and rises to the right.
D) Because the degree is even and the leading coefficient is negative, the graph rises to the left and rises to the right.
E) Because the degree is odd and the leading coefficient is negative, the graph rises to the left and rises to the right.

Question 7

The sum of the length l and the width w of a rectangular region is 180 meters.Write the area A as a function of l.

A)
B)
C)
D)
E)

Question 8

The fuel efficiency, in miles per gallon, for a certain midsize car at various speeds, in miles per hour, is given in the table below. Find a quadratic model for these data.

A)
B)
C)
D)
E)

Question 9

A farmer has 288 feet of fencing and wants to build two identical pens for his prize-winning pigs.The pens will be arranged as shown.Determine the dimensions of a pen that will maximize its area.

A)
B)
C)
D)
E)

Question 10

Determine the vertex of the graph of the quadratic function

A)
B)
C)
D)
E)

Question 11

Find all real zeros of the polynomial and determine the mutiplicity of each.

A) , multiplicity 2; , multiplicity 1; , multiplicity 1
B) , multiplicity 2; , multiplicity 2
C) , multiplicity 2; , multiplicity 1; , multiplicity 1
D) , multiplicity 2; , multiplicity 2
E) , multiplicity 1; , multiplicity 1; , multiplicity 1; , multiplicity 1

Question 12

Graph the given function.

A)
B)
C)
D)
E)

Question 13

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

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

Question 14

The sum of the length l and the width w of a rectangular region is 190 meters.Find the dimensions that produce the greatest area.

A)
B)
C)
D)
E)

Question 15

The height in feet of a projectile with an initial velocity of 96 feet per second and an initial height of 75 feet is a function of time t, in seconds, given by Find the maximum height of the projectile.

A) 254 ft
B) 219 ft
C) 263 ft
D) 105 ft
E) 315 ft

Question 16

The path of a diver is given by where is the height (in feet) and is the horizontal distance from the end of the diving board (in feet).Find the maximum height of the diver.

A) 12 feet
B) 13 feet
C) 10 feet
D) 14 feet
E) 17 feet

Question 17

Compare the graph of with

A) shifts right units, shifts downward units, and shrinks by a factor of
B) shifts right units, shifts upward units, and stretches by a factor of
C) shifts left units, shifts downward units, and stretches by a factor of
D) shifts right units, shifts upward units, and shrinks by a factor of
E) shifts left units, shifts upward units, and stretches by a factor of

Question 18

Examine the leading term and determine the far-left and far-right behavior of the graph of the polynomial function

A) down to the far left, up to the far right
B) down to the far left, down to the far right
C) up to the far left, up to the far right
D) up to the far left, down to the far right
E) cannot be determined

Question 19

The fuel efficiency, in miles per gallon, for a certain midsize car at various speeds, in miles per hour, is given in the table below. Find a quadratic model for these data and use it to predict the fuel efficiency of this car when it is traveling at a speed of 40 mph.Do not round any values in your calculations but round the final answer to the nearest tenth.

A) 33.9 mpg
B) 33.7 mpg
C) 35.7 mpg
D) 32.7 mpg
E) 33.9 mpg

Question 20

Find an equation of the parabola below.

A)
B)
C)
D)
E)

Question 21

Use long division to divide.

A)
B)
C)
D)
E)

Question 22

Write in the form when

A)
B)
C)
D)
E)

Question 23

Use long division to divide.

A)
B)
C)
D)
E)

Question 24

Use long division to divide.

A)
B)
C)
D)
E)

Question 25

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

A)
B)
C)
D)
E)

Question 26

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

A)
B)
C)
D)
E)

Question 27

Find all the real zeros of the polynomial function and determine the multiplicity of each.

A) , multiplicity 2; , multiplicity 1
B) , multiplicity 1; , multiplicity 1; , multiplicity 1
C) , multiplicity 2; , multiplicity 1
D) , multiplicity 1; , multiplicity 1; , multiplicity 1
E) , multiplicity 3

Question 28

Use synthetic division to divide by

A)
B)
C)
D)
E)

Question 29

Use synthetic division to divide.

A)
B)
C)
D)
E)

Question 30

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

A)
B)
C)
D)
E)

Question 31

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?

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

Question 32

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

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

Question 33

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

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

Question 34

Sketch the graph of the polynomial function Do not use a graphing calculator.

A)
B)
C)
D)
E)

Question 35

Match the graph with one of the following functions below. Function I : Function II : Function III : Function IV : Function V :

A) Function I
B) Function IV
C) Function V
D) Function II
E) Function III

Question 36

Use synthetic division to divide.

A)
B)
C)
D)
E)

Question 37

Sketch the graph of the polynomial function below.

A)
B)
C)
D)
E)

Question 38

Use synthetic division to divide.

A)
B)
C)
D)
E)

Question 39

Find the real zeros of the polynomial function and determine the multiplicity of each.

A) , multiplicity 2; , multiplicity 3
B) , multiplicity 2; , multiplicity 1; , multiplicity 2
C) , multiplicity 3; , multiplicity 2
D) , multiplicity 3; , multiplicity 2
E) , multiplicity 2; , multiplicity 2; , multiplicity 1

Question 40

If , use synthetic division to evaluate

A)
B)
C)
D)
E)

Question 41

Simplify the rational expression, , by using long division or synthetic division.

A)
B)
C)
D)
E)

Question 42

Find all the rational zeros of the function

A)
B)
C)
D)
E)

Question 43

Write the complex number in standard form.

A)
B)
C)
D)
E)

Question 44

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

A)
B)
C)
D)
E)

Question 45

Find all real solutions of the polynomial equation

A)
B)
C)
D)
E)

Question 46

Use the Rational Zero Test to list all possible rational zeros of the polynomial function

A)
B)
C)
D)
E)

Question 47

Simplify the rational expression, , by using long division or synthetic division.

A)
B)
C)
D)
E)

Question 48

Find all the real zeros of

A)
B)
C)
D)
E)

Question 49

Find all real solutions of the polynomial equation

A)
B)
C)
D)
E)

Question 50

A farmer wants to enlarge an existing rectangular pig pen such that the total area of the new pen is twice as large as the original pen.The current pen's dimensions are 25' × 27'.The farmer wants to add 13 feet more to the long side than to the the short side.Find the dimensions of the new pen.

A) 5 feet × 18 feet
B) 30 feet × 45 feet
C) 30 feet × 32 feet
D) 30 feet × 43 feet
E) 30 feet × 40 feet

Question 51

An open box is to be made from a square piece of cardboard, 72 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below).After determining the function V, in terms of x, that represents the volume of the box, use a graphing utility to estimate the dimensions that will maximize its volume.

A) × ×
B) × ×
C) × ×
D) × ×
E) × ×

Question 52

Find all the rational zeros of the function

A)
B)
C)
D)
E)

Question 53

Write the complex number in standard form.

A)
B)
C)
D)
E)

Question 54

Evaluate the power of i.

A)
B)
C)
D)
E)

Question 55

The length of a rectangular box is 1 inch more than twice the height of the box, and the width is 3 inches more than the height. If the volume of the box is 440 cubic inches, find the dimensions of the box.

A) 5 in. by 11 in. by 8 in.
B) 4 in. by 9 in. by 7 in.
C) 109 in. by 219 in. by 112 in.
D) 5.5 in. by 12 in. by 8.5 in.
E) 106 in. by 213 in. by 109 in.

Question 56

Find real numbers a and b such that the equation is true.

A)
B)
C)
D)
E)

Question 57

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

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 58

Use the Rational Zero Test to list possible rational zeros for the polynomial function below.

A)
B)
C)
D)
E)

Question 59

Find all the real zeros of

A)
B)
C)
D)
E)

Question 60

A company that produces video games estimates that the profit (in dollars) for selling a new game is given by where is the advertising expense (in tens of thousands of dollars).Using this model, how much should the company spend on advertising to obtain a profit of $6,500,000? Round to the nearest dollar.

A) $399,893 or $744,397
B) $433,844 or $721,190
C) $315,902 or $794,255
D) $368,914 or $764,017
E) $344,417 or $778,509

Question 61

Simplify and write the following complex number in standard form.

A)
B)
C)
D)
E)

Question 62

Combine and write the answer in standard form.

A)
B)
C)
D)
E)

Question 63

Simplify and write the following complex number in standard form.

A)
B)
C)
D)
E) 0

Question 64

Use the quadratic formula to solve

A)
B)
C)
D)
E)

Question 65

Write the polynomial as the product of factors that are irreducible over the rationals.

A)
B)
C)
D)
E)

Question 66

Simplify and write the answer in standard form.

A)
B)
C)
D)
E)

Question 67

Simplify and write the answer in standard form.

A)
B)
C)
D)
E)

Question 68

Simplify and write the answer in standard form.

A)
B)
C)
D)
E)

Question 69

Classify whether the following numbers are in the Mandelbrot Set. I : II : III :

A) Only numbers I and III are in the Mandelbrot Set.
B) Only number II is in the Mandelbrot Set.
C) Only number I is in the Mandelbrot Set.
D) None are in the Mandelbrot Set.
E) Only numbers II and III are in the Mandelbrot Set.

Question 70

Write the following expression as a complex number in standard form.

A)
B)
C)
D)
E)

Question 71

Simplify and write the following complex number in standard form.

A)
B)
C)
D)
E)

Question 72

Simplify and write the answer in standard form.

A)
B)
C)
D)
E)

Question 73

Write as a product of linear factors given that and are zeros of the polynomial.

A)
B)
C)
D)
E)

Question 74

Find all the zeros of the polynomial function and write the polynomial as a product of its linear factors.

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

Question 75

Plot the complex number below.

A)
B)
C)
D)
E)

Question 76

The demand and cost equations for a stethoscope are given by and where is the unit price (in dollars), is the total cost (in dollars), and is the number of units.The total profit (in dollars) obtained by producing and selling units is given by Determine a price that would yield a profit of $4 million.

A) $22.21
B) $44.43
C) $88.85
D) $99.96
E) $66.64

Question 77

Determine the number of zeros of the polynomial function below.

A) 1
B) 3
C) 4
D) 5
E) 6

Question 78

Write as a product of linear factors.

A)
B)
C)
D)
E)

Question 79

Write as a product of linear factors given that and are zeros of the polynomial.

A)
B)
C)
D)
E)

Question 80

Simplify and write the following complex number in standard form.

A)
B)
C)
D)
E)