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Chapter 1: Polynomials Practice Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.

____ 1. Divide:
A.
B.
R(–8)
R8
C.
D.
____ 2. What is the remainder when
A. 515
B. –4
____ 3. Divide
by
A.
B.
C.
D.
=(
=(
=(
=(
A.
B.
)(
)(
)(
)(
D. –45
)
) + 12
)
)–4
, what is the value of
C. 27
as a factor?
C.
D.
____ 6. Factor:
A.
B.
?
. Write the division statement.
B. –69
____ 5. Which polynomial has
is divided by
C. –3
____ 4. For the polynomial
A. 47
R(–8)
R8
C.
D.
?
D. 59
____ 7. When
A. –13
is divided by
B. –5
, the remainder is 1. What is the value of q?
C. 15
____ 8. Which binomial is NOT a factor of
A.
B.
D. 8
?
C.
D.
____ 9. The volume of a shipping box with the shapeof a rectangular prism can be expressed
as the polynomial
. Each dimension of the box can be expressed as a
binomial. Which binomial could represent one dimension of the box?
A.
B.
C.
D.
____10. Use graphing technology. Graph the polynomial function
Which characteristics apply to the graph?
A. Number of x-intercepts: 2
Number of hills: 2
Number of valleys: 1
B. Number of x-intercepts: 2
Number of hills: 1
Number of valleys: 1
.
C. Number of x-intercepts: 1
Number of hills: 1
Number of valleys: 2
D. Number of x-intercepts: 3
Number of hills: 1
Number of valleys: 1
____11. Which statements are always true for both the graphs of cubic functions and the
graphs of quintic functions?
i) The graphs have an odd number of x-intercepts.
ii) The graphs never have equal numbers of hills and valleys.
iii) The values of the constant terms in the equations are the y-intercepts of the graphs.
iv) When the terms with the greatest degree in the equations are negative, the graphs
rise to the left and fall to the right.
A. iii, iv
B. i, ii, iv
C. i, iv
D. i, ii, iii
____12. Which type of polynomial function is f(x) = 2x5 – 2x3 + 7x2?
A. quadratic
B. quartic
C. cubic
D. quintic
____13. The graph of a polynomial function of degree 5 is shown. Which statements are true?
i) The function has an even degree.
ii) The function has two zeros of multiplicity 2.
iii) The equation of the function has a negative leading coefficient.
iv) The y-intercept is positive.
y
0
A. i, ii, iv
x
B. i, ii, iii
C. ii, iii, iv
D. i, iii, iv
____14. Determine the zeros of the polynomial function
multiplicity of each zero.
A.
B.
C.
D.
The zero –5 has multiplicity 3; the zero –4 has multiplicity 2.
The zero 5 has multiplicity 3; the zero 4 has multiplicity 2.
The zero 3 has multiplicity 5; the zero 2 has multiplicity 4.
The zero 3 has multiplicity –5; the zero 2 has multiplicity –4.
. State the
____15. Identify the graph that corresponds to the function
y
A.
C.
32
64
16
32
–8 –6 –4 –2 0
B.
.
y
2
4
6
8
–8 –6 –4 –2
x
–16
–32
–32
–64
y
D.
32
16
–8 –6 –4 –2 0
2
4
6
8
x
2
4
6
8
x
y
32
16
2
4
6
8
–8 –6 –4 –2
x
–16
–16
–32
–32
____16. A carton of juice in the shape of a rectangular prism has dimensions 5.4 cm by 5.4 cm
by 9.2 cm. The manufacturer wants to design a carton with double the capacity by
increasing each dimension by x centimetres. Which equation could be used to
determine the value of x?
A.
B.
C.
D.
Short Answer
1. When
is divided by
Write the division statement.
using synthetic division, the result is:
2. Determine the quotient and remainder when the polynomial
divided by
.
3. Determine one binomial factor of
is
.
4. Graph the polynomial function
Complete the table for the graph.
using graphing technology.
Number
Number of Number
yof
x-intercepts of hills
intercept
valleys
5. Identify each polynomial function as a quadratic, cubic, quartic, or quintic function.
a)
b)
c)
d)
6. Write an equation in standard form for a cubic function with zeros –1, –3, and –4 and
a y-intercept of 6
7. A rectangular prism has dimensions x centimetres,
centimetres, and
centimetres. Determine the maximum volume of the prism to the nearest tenth of a
cubic centimetre.
Problem
1. Is
a factor of
? How do you know?
2. A quartic function has these characteristics: leading coefficient is negative; zero 2 has
multiplicity 2, each of the zeros 1 and 3 has multiplicity 1. Sketch a possible graph
of the function. Justify your thinking. Label the graph with its equation and label the
y-intercept.
3. A cubic function has zeros 2, –1, and –3. The y-intercept of its graph is –12. Sketch
the graph, then determine an equation of the function in standard form. Explain your
work.
4. A rectangular prism has width x units, length
units, and height
Suppose the prism has volume
. Determine its dimensions.
units.
Chapter 1: Polynomials Practice Test
Answer Section
MULTIPLE CHOICE
1. ANS:
D
PTS:
0
DIF:
REF: 1.1 Dividing a Polynomial by a Binomial
TOP: Relations and Functions
KEY:
Procedural Knowledge
Moderate
LOC: 12.RF11
Conceptual Understanding |
2. ANS:
A
PTS:
0
DIF:
REF: 1.1 Dividing a Polynomial by a Binomial
TOP: Relations and Functions
KEY:
Procedural Knowledge
Moderate
LOC: 12.RF11
Conceptual Understanding |
3. ANS:
B
PTS:
0
DIF:
REF: 1.1 Dividing a Polynomial by a Binomial
TOP: Relations and Functions
KEY:
Procedural Knowledge
Moderate
LOC: 12.RF11
Conceptual Understanding |
4. ANS:
Polynomials
LOC:
KEY:
C
Easy REF: 1.2 Factoring
5. ANS:
Polynomials
LOC:
KEY:
C
6. ANS:
Polynomials
LOC:
KEY:
C
7. ANS:
Polynomials
LOC:
KEY:
A
PTS:
0
DIF:
12.RF11
TOP: Relations and Functions
Conceptual Understanding | Procedural Knowledge
PTS:
0
DIF:
Easy REF: 1.2 Factoring
12.RF11
TOP: Relations and Functions
Conceptual Understanding | Procedural Knowledge
PTS:
0
DIF:
Difficult
REF: 1.2 Factoring
12.RF11
TOP: Relations and Functions
Conceptual Understanding | Procedural Knowledge
PTS:
0
DIF:
Moderate REF: 1.2 Factoring
12.RF11
TOP: Relations and Functions
Conceptual Understanding | Problem-Solving Skills
8. ANS:
Polynomials
LOC:
KEY:
A
9. ANS:
Polynomials
LOC:
KEY:
A
PTS:
0
DIF:
Moderate REF: 1.2 Factoring
12.RF11
TOP: Relations and Functions
Conceptual Understanding | Procedural Knowledge
PTS:
0
DIF:
Difficult
REF: 1.2 Factoring
12.RF11
TOP: Relations and Functions
Procedural Knowledge | Problem-Solving Skills
10. ANS:
B
PTS:
0
DIF:
Easy REF: 1.3 Graphing
Polynomial Functions
LOC:
12.RF12
TOP: Relations and Functions
KEY:
Conceptual Understanding | Procedural Knowledge
11. ANS:
A
PTS:
Polynomial Functions
LOC:
12.RF12
Conceptual Understanding
0
DIF:
Moderate REF: 1.3 Graphing
TOP: Relations and Functions
KEY:
12. ANS:
D
PTS:
0
DIF:
Easy
REF: 1.4 Relating Polynomial Functions and Equations LOC: 12.RF12
TOP: Relations and Functions
KEY:
Conceptual Understanding
13. ANS:
C
PTS:
0
DIF:
Moderate
REF: 1.4 Relating Polynomial Functions and Equations LOC: 12.RF12
TOP: Relations and Functions
KEY:
Conceptual Understanding
14. ANS:
A
PTS:
0
DIF:
Easy
REF: 1.4 Relating Polynomial Functions and Equations LOC: 12.RF12
TOP: Relations and Functions
KEY:
Conceptual Understanding
15. ANS:
D
PTS:
0
DIF:
Moderate
REF: 1.4 Relating Polynomial Functions and Equations LOC: 12.RF12
TOP: Relations and Functions
KEY:
Conceptual Understanding |
Procedural Knowledge
16. ANS:
C
PTS:
0
DIF:
Moderate
REF: 1.5 Modelling and Solving Problems with Polynomial Functions
LOC:
KEY:
12.RF12
TOP: Relations and Functions
Procedural Knowledge | Problem-Solving Skills
SHORT ANSWER
1. ANS:
PTS: 0
LOC:
KEY:
DIF: Easy
REF: 1.1 Dividing a Polynomial by a Binomial
12.RF11
TOP: Relations and Functions
Conceptual Understanding | Procedural Knowledge
2. ANS:
R(–4)
PTS: 0
LOC:
KEY:
3. ANS:
,
PTS: 0
LOC:
KEY:
DIF: Moderate REF: 1.1 Dividing a Polynomial by a Binomial
12.RF11
TOP: Relations and Functions
Conceptual Understanding | Procedural Knowledge
, or
DIF: Moderate REF: 1.2 Factoring Polynomials
12.RF11
TOP: Relations and Functions
Conceptual Understanding | Procedural Knowledge
4. ANS:
Number
Number of Number
yof
x-intercepts of hills
intercept
valleys
3
1
1
5
PTS: 0
LOC:
KEY:
DIF: Easy
REF: 1.3 Graphing Polynomial Functions
12.RF12
TOP: Relations and Functions
Procedural Knowledge | Communication
5. ANS:
a) cubic function
b) quintic function
c) quadratic function
d) quartic function
PTS: 0
DIF: Easy
Equations
LOC:
12.RF12
Conceptual Understanding
REF: 1.4 Relating Polynomial Functions and
TOP: Relations and Functions
KEY:
6. ANS:
Answers may vary by a common numerical factor.
For example:
PTS: 0
Equations
LOC:
KEY:
DIF: Moderate REF: 1.4 Relating Polynomial Functions and
12.RF12
TOP: Relations and Functions
Procedural Knowledge | Communication
7. ANS:
PTS: 0
DIF: Moderate
REF: 1.5 Modelling and Solving Problems with Polynomial Functions
LOC:
12.RF12
TOP: Relations and Functions
KEY:
Procedural Knowledge | Problem-Solving Skills
PROBLEM
1. ANS:
Let
is a factor of
Since P(2) is 0,
PTS: 0
LOC:
KEY:
.
if
.
is a factor of
.
DIF: Easy
REF: 1.2 Factoring Polynomials
12.RF11
TOP: Relations and Functions
Procedural Knowledge | Communication
2. ANS:
The zero 2 has multiplicity 2, so the graph just touches the x-axis at
.
Each of the zeros 1 and 3 has multiplicity 1, so the graph crosses the x-axis at
and
.
Since the function is quartic, there are no more zeros.
The leading coefficient is negative, so as
, the graph falls to the left, and as
, the graph falls to the right. That is, the graph opens down.
A possible graph is:
y
–3
–1 0
2
x
–12
A possible equation is:
The y-intercept for this function is:
PTS: 0
Equations
LOC:
KEY:
DIF: Moderate REF: 1.4 Relating Polynomial Functions and
12.RF12
TOP: Relations and Functions
Conceptual Understanding | Communication
3. ANS:
Sketch the graph:
y
–3
–10
2
x
–12
The zeros of the function are the roots of its related polynomial equation.
Let k represent the leading coefficient.
The constant term in the equation is –12.
So,
So, an equation is:
PTS: 0
Equations
LOC:
KEY:
DIF: Moderate REF: 1.4 Relating Polynomial Functions and
12.RF12
TOP: Relations and Functions
Procedural Knowledge | Communication
4. ANS:
The prism has dimensions 9 units by 16 units by 26 units.
PTS: 0
DIF: Moderate
REF: 1.5 Modelling and Solving Problems with Polynomial Functions
LOC:
12.RF12
TOP: Relations and Functions
KEY:
Procedural Knowledge | Problem-Solving Skills