Name: 
 

AII.8 - Solutions, Zeros, and Factors



Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1 

Which phrase describes the roots of the equation mc001-1.jpg?
a.
Exactly 2 distinct real roots
c.
Exactly 1 distinct root
b.
Exactly 2 distinct imaginary roots
d.
Exactly 1 real root and 1distinct imaginary root.
 

 2 

Which phrase describes the roots of the equation mc002-1.jpg?
a.
Exactly 2 distinct real roots
c.
Exactly 3 distinct roots
b.
Exactly 2 distinct imaginary roots
d.
Exactly 1 real root and 2 distinct imaginary roots.
 

 3 

Which phrase describes the roots of the equation mc003-1.jpg?
a.
Exactly 2 distinct real roots
c.
Exactly 1 distinct root
b.
Exactly 2 distinct imaginary roots
d.
Exactly 1 real root and 1distinct imaginary root.
 

 4 

A polynomial function P(x) has zeros mc004-1.jpg.  Which of the following represents the factors of P(x)?
a.
mc004-2.jpg
b.
mc004-3.jpg
c.
mc004-4.jpg
d.
mc004-5.jpg
 

 5 

Identify the equation that best represents the graph p(x).
mc005-1.jpg
a.
mc005-2.jpg
b.
mc005-3.jpg
c.
mc005-4.jpg
d.
mc005-5.jpg
 

 6 

Choose one of these phrases to describe the roots of the function mc006-1.jpg.
a.
2 distinct real roots
b.
2 distinct imaginary roots
c.
3 distinct real roots
d.
exactly 1 real root and 2 distinct imaginary roots
 

 7 

Write the equation of the graph shown as a product of the factors.

mc007-1.jpg
a.
mc007-2.jpg
c.
mc007-4.jpg
b.
mc007-3.jpg
d.
mc007-5.jpg
 

 8 

A polynomial function has a zero at   x = 3.   Which of the following expressions
must be one factor of the polynomial?
a.
mc008-1.jpg
b.
mc008-2.jpg
c.
mc008-3.jpg
d.
mc008-4.jpg
 

Multiple Response
Identify one or more choices that best complete the statement or answer the question.
 

 9 

Directions: Click on a box to choose each factor you want to select.  You must select all correct factors. 

The zeros of a cubic function f(x) are -1, mr009-1.jpg, and 5.  Select all of the factors of f(x).
 a.
(x - 1)
 d.
(x + 1)
 b.
(3x + 2)
 e.
(3x - 2)
 c.
(x + 5)
 f.
(x - 5)
 

 10 

Choose all the statements that are true based on the graph below.
mr010-1.jpg
 a.
The zeros are -7 and 9.
 b.
The solutions to the equation represented by the graph when mr010-2.jpg are x = -7 and x = 9
 c.
The x-intercepts of the function are (0, -7) and (0, 9).
 d.
The factored form of the function would include the factors (x +7) and (x - 9).
 



 
Check Your Work     Start Over