Question 1

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

Accepted Answer

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

Question 2

Find a polynomial with the given zeros.

Accepted Answer

A)    
B)    
C)    
D)    
E)  none of these 
A)    
B)    
C)    
D)    
E)  none of these

Question 3

Simplify the expression. i -2

Accepted Answer

A)  - i 
B)  - 1 
C)  i 
D)  - 3i 
E)  1 
A)  - i 
B)  - 1 
C)  i 
D)  - 3i 
E)  1

Question 4

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

Accepted Answer

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 
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 5

Graph the polynomial function.

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

Find all zeros of the function   .

Accepted Answer

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

Question 8

Find the vertex of the parabola. y = 6x2 - 4

Accepted Answer

A)  (0, -4) 
B)  (-4, 0) 
C)  (0, 6) 
D)  (6, -4) 
E)  (-4, 6) 
A)  (0, -4) 
B)  (-4, 0) 
C)  (0, 6) 
D)  (6, -4) 
E)  (-4, 6)

Question 9

Let   . Use synthetic division to find the value   .

Accepted Answer

A)    
B)    
C)    
D)    
E)  none of these 
A)    
B)    
C)    
D)    
E)  none of these

Question 10

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

Accepted Answer

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

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.

Accepted Answer

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

Question 12

Graph the function.

Accepted Answer

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

Question 13

Find the standard form of the quadratic function shown below:

Accepted Answer

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

Question 14

Find all zeros of the function   .

Accepted Answer

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

Question 15

Write   in the form   when   .

Accepted Answer

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

Question 16

Find all the real zeros of   .

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

Tell whether the function   is even or odd. If it is neither, so indicate.

Accepted Answer

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

Question 19

Find a polynomial with the given zeros.

Accepted Answer

A)    
B)    
C)    
D)    
E)  none of these 
A)    
B)    
C)    
D)    
E)  none of these

Question 20

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

Accepted Answer

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 
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

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

Find a polynomial with the given zeros.

Simplify the expression. i^-2

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

Graph the polynomial function.

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

Find all zeros of the function .

Find the vertex of the parabola. y = 6x² - 4

Let . Use synthetic division to find the value .

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

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.

Graph the function.

Find the standard form of the quadratic function shown below:

Find all zeros of the function .

Write in the form when .

Find all the real zeros of .

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

Tell whether the function is even or odd. If it is neither, so indicate.

Find a polynomial with the given zeros.

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

Functions and Their Graphs

Solving Equations and Inequalities

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Prerequisites

Filters

Exam 3: Polynomial and Rational Functions

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

Find a polynomial with the given zeros.

Simplify the expression. i -2

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

Graph the polynomial function.

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

Find all zeros of the function .

Find the vertex of the parabola. y = 6x2 - 4

Let . Use synthetic division to find the value .

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

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.

Graph the function.

Find the standard form of the quadratic function shown below:

Find all zeros of the function .

Write in the form when .

Find all the real zeros of .

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

Tell whether the function is even or odd. If it is neither, so indicate.

Find a polynomial with the given zeros.

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

Functions and Their Graphs

Solving Equations and Inequalities

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Prerequisites

Filters

Simplify the expression. i^-2

Find the vertex of the parabola. y = 6x² - 4