Deck 3: Polynomial and Rational Functions

Question 1

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

A) 3 positive reals or 1 positive real; no negative reals
B) no positive reals; no negative reals
C) 1 positive real; 3 negative reals or 1 negative real
D) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real
E) 0 positive real; 3 negative reals or 1 negative real

Answer 1

0 positive real; 3 negative reals or 1 negative real

Question 2

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

A)
B)
C)
D)
E)

Answer 2

Question 3

Find the standard form of the quadratic function shown below:

A)
B)
C)
D)
E)

Answer 3

Question 4

Find all the rational zeros of the function .

A)
B)
C)
D)
E)

Question 5

Write the standard form of the equation of the parabola that has a vertex at and passes through the point .

A)
B)
C)
D)
E)

Question 6

Use synthetic division to divide.

A)
B)
C)
D)
E)

Question 7

Find all the real zeros of .

A)
B)
C)
D)
E)

Question 8

Graph the given function.

A)
B)
C)
D)
E)

Question 9

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

A)
B)
C)
D)
E)

Question 10

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

A) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real
B) 3 positive reals or 1 positive real; no negative reals
C) no positive reals; no negative reals
D) 3 positive reals or 1 positive real; 1 negative real
E) 1 positive real; 3 negative reals or 1 negative real

Question 11

An open box is to be made from a square piece of cardboard, 35 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.

A)
B)
C)
D)
E)

Question 12

Use long division to divide.

A)
B) 4x - 1
C)
D)
E)

Question 13

Using a graphing utility, graph and approximate the zeros and their multiplicity.

A)
B)
C)
D)
E)

Question 14

Write in the form when .

A)
B)
C)
D)
E)

Question 15

Find all the real zeros of .

A)
B)
C)
D)
E)

Question 16

A farmer has 240 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 17

If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

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

Question 18

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

A)
B)
C)
D)
E)

Question 19

Determine the vertex of the graph of the quadratic function .

A)
B)
C)
D)
E)

Question 20

Write the standard form of the equation of the parabola that has a vertex at and passes through the point .

A)
B)
C)
D)
E)

Question 21

An open box is to be made from a square piece of cardboard, 35 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.

A)
B)
C)
D)
E)

Question 22

Using a graphing utility, graph and approximate the zeros and their multiplicity.

A)
B)
C)
D)
E)

Question 23

Write the standard form of the equation of the parabola that has a vertex at and passes through the point .

A)
B)
C)
D)
E)

Question 24

Determine the vertex of the graph of the quadratic function .

A)
B)
C)
D)
E)

Question 25

Write as a product of linear factors.

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

Write as a product of linear factors.

A)
B)
C)
D)
E)

Question 28

A farmer has 240 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 29

Write in the form when .

A)
B)
C)
D)
E)

Question 30

Find all zeros of the function .

A)
B)
C)
D)
E)

Question 31

Graph the given function.

A)
B)
C)
D)
E)

Question 32

Use synthetic division to divide.

A)
B)
C)
D)
E)

Question 33

Determine the zeros (if any) of the rational function .

A)
B)
C) no zeros
D)
E)

Question 34

If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

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

Question 35

Write the standard form of the equation of the parabola that has a vertex at and passes through the point .

A)
B)
C)
D)
E)

Question 36

Find all zeros of the function .

A)
B)
C)
D)
E)

Question 37

Use long division to divide.

A)
B)
C)
D)
E) 4x - 3

Question 38

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

A)
B)
C)
D)
E)

Question 39

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

A)
B)
C)
D)
E)

Question 40

Find the standard form of the quadratic function shown below:

A)
B)
C)
D)
E)

Question 41

Find all the real zeros of .

A)
B)
C)
D)
E)

Question 42

Find the standard form of the quadratic function shown below:

A)
B)
C)
D)
E)

Question 43

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

A) 3 positive reals or 1 positive real; no negative reals
B) 1 positive real; 3 negative reals or 1 negative real
C) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real
D) no positive reals; no negative reals
E) 0 positive real; 3 negative reals or 1 negative real

Question 44

A farmer has 336 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 45

Find all zeros of the function .

A)
B)
C)
D)
E)

Question 46

An open box is to be made from a square piece of cardboard, 21 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.

A)
B)
C)
D)
E)

Question 47

Find all the rational zeros of the function .

A)
B)
C)
D)
E)

Question 48

Using a graphing utility, graph and approximate the zeros and their multiplicity.

A)
B)
C)
D)
E)

Question 49

Find all the real zeros of .

A)
B)
C)
D)
E)

Question 50

Determine the vertex of the graph of the quadratic function .

A)
B)
C)
D)
E)

Question 51

Write the standard form of the equation of the parabola that has a vertex at and passes through the point .

A)
B)
C)
D)
E)

Question 52

Determine the zeros (if any) of the rational function .

A) no zeros
B)
C)
D)
E)

Question 53

Find all zeros of the function .

A)
B)
C)
D)
E)

Question 54

Write as a product of linear factors.

A)
B)
C)
D)
E)

Question 55

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

A)
B)
C)
D)
E)

Question 56

Write as a product of linear factors.

A)
B)
C)
D)
E)

Question 57

Write the standard form of the equation of the parabola that has a vertex at and passes through the point .

A)
B)
C)
D)
E)

Question 58

Graph the given function.

A)
B)
C)
D)
E)

Question 59

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

A) 3 positive reals or 1 positive real; 1 negative real
B) 3 positive reals or 1 positive real; no negative reals
C) no positive reals; no negative reals
D) 1 positive real; 3 negative reals or 1 negative real
E) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real

Question 60

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

A)
B)
C)
D)
E)

Question 61

Find all zeros of the function .

A)
B)
C)
D)
E)

Question 62

Find the vertex of the parabolic graph of the equation. y = 6(x - 7) ² + 4

A) (49, 4)
B) (7, 6)
C) (4, 7)
D) (7, 4)
E) (7, 0)

Question 63

Graph the quadratic function. f (x) = x² + 3x

A)
B)
C)
D)

Question 64

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

A) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real
B) 3 positive reals or 1 positive real; no negative reals
C) 1 positive real; 3 negative reals or 1 negative real
D) 3 positive reals or 1 positive real; 1 negative real
E) no positive reals; no negative reals

Question 65

Graph the quadratic function.

A)
B)
C)
D)

Question 66

Find all zeros of the function .

A)
B)
C)
D)
E)

Question 67

Find all the rational zeros of the function .

A)
B)
C)
D)
E)

Question 68

Write as a product of linear factors.

A)
B)
C)
D)
E)

Question 69

Graph the quadratic function. f (x) = - 3x² + 2

A)
B)
C)
D)

Question 70

Find all the real zeros of .

A)
B)
C)
D)
E)

Question 71

Write in the form when .

A)
B)
C)
D)
E)

Question 72

Determine the zeros (if any) of the rational function .

A)
B)
C)
D)
E) no zeros

Question 73

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

A)
B)
C)
D)
E)

Question 74

Find the vertex of the parabola. y = 9x² - 10

A) (0, -10)
B) (0, 9)
C) (9, -10)
D) (-10, 0)
E) (-10, 9)

Question 75

Use synthetic division to divide.

A)
B)
C)
D)
E)

Question 76

If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

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

Question 77

Find all the real zeros of .

A)
B)
C)
D)
E)

Question 78

Write as a product of linear factors.

A)
B)
C)
D)
E)

Question 79

Use long division to divide.

A)
B)
C)
D)
E) -x + 2

Question 80

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

A) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real
B) 3 positive reals or 1 positive real; no negative reals
C) 0 positive real; 3 negative reals or 1 negative real
D) 1 positive real; 3 negative reals or 1 negative real
E) no positive reals; no negative reals