Sample of College-Level Math Attributes in College Algebra
Prepared by:
Nancy Priselac, Garrett College;
Bob Carson, Hagerstown Community College;
Debra Loeffler, Community College of Baltimore County
Course Description:
Students will study the nature and scope of college mathematics through the study of real valued functions.
Topics include graphing functions, equations and inequalities, polynomials and rational functions, inverse functions, and
exponential/ logarithmic functions. Applications to real life are discussed.
Typical Outcomes:
Students successfully completing this course will be able to:
1.
2.
3.
4.
5.
6.
Gain facility in factoring, radicals, absolute values, literal equations, rationals, variation, exponential and logs.
using algebraic/geometric skills.
Find solutions for linear, quadratic, cubic, quartic,, exponential, rational equations, and inequalities.
Identify types of relations/functions, e.g. polynomials, rationals, radicals, exponentials, logs, absolute value,
and greatest integer.
Graph relations and functions using information about the functions, such as, zeros and properties, e.g.
increasing, decreasing, asymptotes, intercepts, symmetry, shifts.
Perform operations on relations and functions, e.g. addition, subtraction, multiplication, division,
composition, inverses.
Solve equations and inequalities containing two or more unknowns.
Several of the following topics will also be required.
1.
Combinations, sequences, and series, e.g. expanding a binomial using the binomial theorem.
2.
Partial Decomposition
3.
Conics
C1
Graphing & Function Notation
Attributes
1
1,4
College Algebra
Determine whether the points A(-2,2), B(4,-3), and C(-2,-2) are
vertices of a right triangle. Use a figure to explain your answer
mathematically using core concepts to validate your conclusion.
(Keedy and Bittinger 140).
A manufacturer of custom windows uses rows and columns of oneunit panes, where the number of rows is always 1 greater than the
number of columns. The cost of a window is $45 per unit pane.
a. If a window has x columns, how is the number of rows
represented? Then what expression represents the total
number of one-unit panes?
b. Write a function C for the cost of a window with x columns.
c. If a window can have no more than 6 rows, what is the
domain of function C?
d. Evaluate C to determine the total cost of a window with 4
columns.
(Hubbard/Robinson 126)
1,4
The table below gives the total amount of bottled water consumed
annually (in billions of gallons) by Americans for each year from
1996 to 2001.
Year
Consumptio
n
1996
3.5
1997
3.8
1998
4.2
1999
4.6
2000
4.9
2001
5.5
a. Create a scatterplot of the data, with year on the horizontal
axis. Sketch a line on your scatterplot representing the linear
trend.
b. Write the equation of a linear function that models annual
consumption, C, as a function of t, where t represents the
number of years since 1995.
c. According to your model, by how much is Americans’
bottled water consumption increasing each year?
d. Use your model to find the value of C when t = 7. Explain
what this means.
e. According to your model, in what year will total
bottled water consumption exceed six billion
gallons? What assumptions do you need to make?
Note Skills needed from Intermediate Algebra:
Linear equations, solving linear equations for the dependent
variable, graphing lines and points, slope, etc.
C2
Intermediate Algebra
Topics from Introductory Algebra are
reviewed and extended. Distance
between two points and the midpoint of
a line segment are introduced.
Numerically some of the problems
involve points whose coordinates are
irrational numbers. Fitting lines to data
and correlation are introduced.
Application problems are more
complicated than those of Introductory
Algebra. The hardest application
problems for students are typified by
the following:
If (2, 0) and (0, 5) are points on the
graph of
y = mx + b, what are m and b?
Each Sunday, a newspaper agency
sells x copies of a certain newspaper
for $1.00 per copy. The cost to the
agency of each newspaper is $0.50.
The agency pays a fixed cost for
storage, delivery, and so on of $100
per Sunday.
a. Write the equation that relates the
profit P, in dollars, to the number x of
copies sold.
b. Graph your equation.
a. What is the profit to the company,
if 5000 copies are sold?
An economist wishes to estimate a line,
which relates personal consumption
expenditures (C) and disposable
income (I). Both C and I are in
thousands of dollars. She interviews 8
heads of households for families of size
four and obtains the following data:
C| 16 18 13 21 27 26 36 39
I| 20 20 18 27 36 37 45 50
Let I represent the independent
variable.
a. Use a graphing utility to draw a
scatter plot.
b. Use a graphing utility to fit a
straight line to the data.
c. Interpret the slope. The slope of
this line is called the marginal
propensity to Income.
d. Predict the consumption of a
family whose disposable income is
$42,000.
C3
2
To determine when a forest should be harvested, forest managers
often use formulas to estimate the number of board feet a tree will
produce. A board foot equals 1 square foot of wood, 1 inch thick.
Suppose that the number of board feet y yielded by a tree can be
estimated by y=f(x)=15+0.004(x-10)3 where the diameter of the tree
in inches measured at a height of 4 feet above the ground. Graph
y=f(x) for 10≤x≤25.
1
Partial Fractions:
Decompose into partial fractions
5x + 7
x2 + 2x - 3
1,4
The data in the table below gives the results of a study that was
conducted to determine the relationship between average hours of
sleep per night and death rate per 100,000 males.
Hours
of Sleep
Death
Rate
2,3
5
1121
Death Rate related to Sleep
6
7
8
9
769
626
692
967
Graphing of quadratic equations is
extended to include recognizing when
a quadratic equation has complex
solutions. Students should be asked to
recognize the shape of other
polynomial function, in particular
cubic and quartic equations, and
identify its maximum number of roots.
In addition, they may be asked to find
the x-intercepts for some cubic and
quartic equations by factoring.
Graphing calculators may be used to
estimate intercepts and max/min
points. Graphing of rational functions
shall be introduced along with the
concept of asymptotes. Use of a
calculator to fit a quadratic, cubic or
quartic equation to a data set may be
required. The hardest application
problems for students are typified by
the following:
Graph the following functions, finding
approximate and exact values (if
possible) for the x- and y-intercepts.
Determine the multiplicity of the roots,
the power function the graph resembles
for large values of x, the number of
turning points and any asymptotes.
Estimate all local maxima and minima.
f ( x)  ( x  1) 2 ( x  3)( x  1) ,
a. Use the method of finite differences to explain why a
quadratic model would be appropriate for the relationship
between death rate and average hours of sleep per night.
b. Write the equation of a quadratic function that models death
rate, D, as a function of average hours of sleep, h.
c. Use your model to find the amount of sleep per night (to the
nearest tenth of an hour) that would correspond to the lowest
x2  x  6
, and
R( x )  2
death rate. What would the death rate be for this amount of
x  x6
sleep?
3
2
.
d. Give a possible reason why death rate goes up as the amount f ( x)  12 x  39.8x  4.4 x  34
of sleep per night increases beyond the optimal level.
Explain how you tell from its equation
e. Would stating that men should avoid sleeping more than
that a polynomial is a parabola.
seven or eight hours a night in order to lower their chances
of death be a valid conclusion from this study? Explain.
The height H, in feet, of a projectile
with an initial velocity of 96 ft./sec
launched from 120 ft. above ground
Given f and g described by f(x) = 8 – x and g (x) = √(2x + 3)
level is given by the equation
a. Find (f+g)(5) and (f+g)(-4)
H  16t 2  96t  120 , where t = time in
seconds. Sketch the graph of this
b. Do both exist as real numbers? Explain.
function and find the following.
a. How many seconds after the
(Keedy/Bittinger 1190)
launch is the projectile 128 ft.
above the ground?
b. What is the projectile’s
Note Skills needed from Intermediate Algebra:
maximum height and when
Parabolas, graphing non-linear functions, solving quadratic
does it reach that height?
equations, etc.
c. How many seconds after the
launch does the projectile
C4
return to the ground?
2
Ellipses: Sketch the graph of each equation, find the coordinates of
the foci, and find the lengths of the major and minor axis.
9x2 + 16y2 = 144 and 2x2 + y2 = 10
3,5
How far can you see to the horizon through an airplane window at a
height of 30,000 ft?
3,5
A person can see 144 miles to the horizon from an airplane window.
How high is the airplane?
(Keedy and Bittinger, 114-115)
Use a graphing calculator to estimate the real solutions to the
following equations and, if possible, find the exact solutions
algebraically.
3
2 x  4  2, and
Find the center and radius of the
following circle and sketch its graph:
2 x 2  2 y 2  12 x  8 y  24  0 .
Equations containing radicals are often
introduced in Intermediate Algebra.
The hardest problems for students
concerning equations containing
radicals are typified by the following:
Distance to the horizon. The formula
V = 1.2 √h can be used to approximate
the distance V, in miles, that a person
can see to the horizon from a height h,
in feet.
2x  3  x  2  2
2
Find the domain N(x) = 1/ 3√ (x2 – 1)
2
Express h as a composition of two simpler functions f and g of the
form f(x) = xn and g(x) = ax + b where n is a rational number and a
and b are integers.
H(x) = (4/√x) +3
2
Graphing of circles and finding their
center and radius are introduced. In
addition, parabolas, ellipses, and
hyperbolas may be introduced. The
hardest application problems for
students concerning circles are typified
by the following:
Functions are defined, along with
function notation. The concept of
domain and range are introduced.
Composition of functions is also
defined. The hardest problems for
students concerning function notation
are typified by the following:
A time management consultant finds that the length L of a meeting
(in minutes) can be modeled by the function L(n) = 10(n2-n), where
n is the number of people (up to 5) attending the meeting.
Find the domain and range of the
a. For this situation, what is the domain of L?
b. Create a table with the headings Number of People and
Length of Meeting. Then complete the table by evaluating
L.
c. Although 1 is not a meaningful domain element in this
situation, evaluate and interpret L(1).
(Hubbard/Robinson 121)
Find f  g( x) if,
When a stone is dropped into a pond, the radius of the circular
ripple increases at a rate of 1.5 feet per second.
a. Write a function r to describe the length of the radius at time
t (in seconds).
b. Write a function A that describes the area enclosed by the
ripple in terms of the radius r.
c. Write a composite function f that gives the area of the ripple
C5
function f ( x)  x 2  x  6 .
f ( x) 
x 1
x
and g( x) 
.
x3
2 x
as a function of time t.
d. To the nearest tenth, what is the area of the ripple after 2.5
seconds?
(Hubbard/Robinson 292)
2
Graph each equation. Explain if a function, describe any
similarities and differences:
Y2 = 8x
16x2 + 25 y2 = 400
9y2 – 16x2 = 144
Families of functions such as
y  f ( x)  c, y  f ( x  c), and y  f ( kx)
are introduced. Symmetry about the xaxis, y- axis and origin are usually
covered.
1,4
The table gives the total number of stock funds and bond funds in
selected years. (Source: Investment Company Institute.)
Year
Number of funds
1991
244
1993
653
1994
756
1996
541
a. By examining a scatterplot of the data, decide what type of
model is appropriate.
b. Let x represent the number of years since 1990 and
determine a quadratic regression equation to model the data.
(Round coefficients to the nearest integer.)
c. Use the model to estimate the year(s) in which the number
of funds is approximately 400.
d. Estimate and interpret the vertex of the graph of the model
function.
(Hubbard/Robinson 189)
1
A function f is given. In parts a and b, produce the graphs of the
associated functions in the same coordinate system and describe the
graphs in comparison to the graph of f. In part c, write a function
whose graph is described.
1
f(x) = x3
a. g(x) = (x + c)3 for c = -4, 1, 2
b. h(x) = -x3 + c for c = -8, -2, 3
c. The graph of y = -x3 shifted left 4 units
(Hubbard/Robinson 214)
Consider the expression x2 – 2x + c, where c is a number of your
choosing.
a. Produce the graphs of this expression for c-values that are
less than 1. Which points of the graphs represent solutions
of the equation x2 – 2x + c = 0?
b. Repeat this experiment for c = 1 and for c >1.
c. From the results in parts a and b, what is your conjecture
about the possible number of real number solutions of a
quadratic equation?
(Hubbard/Robinson 90)
C6
In intermediate algebra students are
often asked to solve quadratic and
rational inequalities of the type
f ( x)  0, f ( x)  0, f ( x)  0 and f ( x)  0 ,
and to graph inequalities of the type
y  f ( x), y  f ( x), y  f ( x) and
y  f ( x) for functions such as:
f ( x)  x 2  2 x  6, and f ( x) 
1
2

x  1 7x  4
.
Note: sometimes these skills may be
asked for indirectly in problems such
as ones asking student to find the
domain and range of the functions,
expressing their answers in interval
notation.
C7
1
Find the inverse of f(x) = 4x – x2, x ≥ 2.
Graph f, f-1 and y = x in the same coordinate system.
1
Let f(x) = √(x + 2). Determine a rule for f-1
(Hubbard/Robinson 301)
2x  5
. Use interval
x3
notation to state the domain and range of both f ( x) and f 1 ( x) .
Find the inverse, f 1 ( x) , of the function f ( x) 
In a short paragraph, explain the procedure you should use to find
the inverse of a function.
2
Find a piecewise function of f (x) that does not involve the absolute
value function. Sketch the graph, and find the domain and range
and any points of discontinuity.
2
Graph: f(x) = │x│/x
3,5
Solve: │3u - 2│ = u2
2
Bacterial Growth: If bacteria in a certain culture double every ½ hr,
write an equation that gives the number of bacteria N in the culture
after t hours, assuming culture has 100 bacteria at the start. Graph
the equation for 0≤t≤5.
2
Solve each equation:
(x-3)ex=0
3,5
 1 

 x 1
Find the domain of f  x   ln 
(Sullivan, 426)
Solve log3 243  2 x  1
(Sullivan, 427)
Note Skills needed from Intermediate Algebra:
Finding, graphing and determining exponential functions, using
logarithms as an inverse to exponential functions, etc.
Students should be able to recognize
one-to-one functions, find the graph of
their inverse as the reflection across the
line y = x, and find their inverse
algebraically. Students should also
understand the relationship between the
domain and range of a function, and
that of its inverse function. The
hardest problems for students
concerning inverse functions are
typified by the following:
In Intermediate Algebra, students may
be asked to solve both graphically and
algebraically absolute value equations
or inequalities, such as, 3x  2  0.02 .
The greatest integer function is
sometimes introduced in Intermediate
Algebra.
Exponential functions are usually
introduced in Intermediate Algebra.
Log functions are defined as the
inverse of the exponential function;
however, the laws of logarithms are not
usually stressed. Students are expected
to recognize both types of functions
and to graph them. The hardest
problems for students concerning
exponential and log functions are
typified by the following:
A model for the number of people N in
a community college who have heard a
certain rumor is N = Pe-0.15d, where P is
the total population of the community
college and d is the number of days
that have elapsed since the rumor
began. In a community of 1000
students, find the following:
a. How many students will have
heard the rumor after 3 days?
b. How many days will have
elapsed before 450 students
have heard the rumor?
The model year and prices of used
Honda Accords are given in the table
below (not shown). Draw a scatter
plot of this data and use your
calculator to find the equation of the
curve that best fits this data. (Note to
C8
the reader: the data fits an exponential
function.)
3,5
SOLVING EQUATIONS AND INEQUALITIES
Intermediate Algebra
Going into the final exam, which will count as 2/3 of the
The topics from Introductory Algebra are
final grades, Mike has test scores of 86, 80, 84, and 90. What reviewed and extended in a condensed format.
score does Mike need on the final in order to earn a B, which The types of problems given are of a more
requires an average score of 80? What does he need to earn
complex nature. Work problems with more in
an A, which requires an average of 90?
depth reasoning are focused on. Typical
(Sullivan 103)
examples:
Suppose that the speed limit on a long stretch of interstate is
70 mph.
a. Write a function f to describe the distance traveled in
t hours if the driver maintains a constant speed that
exceeds the speed limit by 10 mph.
b. Write a function s to describe the distance traveled in
t hours if the driver maintains a constant speed at the
speed limit.
c. Evaluate and interpret (f – s)(2).
(Hubbard/Robinson 292)
3,5
Solve for r, if S 
In a class of 62 students, the number of
females is one less than twice the number of
males. How many females and how many
males are there in the class?
A sum of $10,000 is split between 2
investments, one pays 9%, another pays 11%.
If the return of the 11% investment is 60
dollars more per year than the 9%, how much
is in each fund?
Equations that contain more than one variable
are referred to as literal equations. Sometimes
referred to as formulas. Practice is given in
solving for a given variable, i.e., solving E =
mc2 for m. Sample application problems
would be:
a
1 r
(Sullivan 94)
How many gallons of a 15% salt solution need
to be mixed with a 35% salt solution to obtain
8 gallons of 30% salt solution?
C9
3,5
1
1
The force F (in newtons) required to maintain an object in a
circular path varies jointly with the mass m (in kilograms) of
the object and the square of its speed v (in meters per second)
and inversely with the radius r (in meters) of the circular
path. The constant of proportionality is 1. Write an equation
relating F, m, v, and r. A motorcycle with mass 150
kilograms is driven at a constant speed of 120 kilometers per
hour on a circular track with a radius of 100 meters. To keep
the motorcycle from skidding, what frictional force must be
exerted by the tires on the track?
Most texts have a section or unit on direct and
inverse variation or proportionality between
two variables, and they discuss the constant of
proportionality application problems. They
include problems from all areas of science.
Typical examples of problems students find
the hardest are:
(Sullivan, 198)
The volume of gas (V) varies directly as
temperature (T) and inversely as pressure (p).
Set up equation and evaluate the constant of
proportionality of V = 48 when T = 320 and
P= 20.
The focus of each method is reviewed. A
discussion of the discriminate to predict the
number of solutions is generally gone over
and the applications go into more depth.
Quadratic equations with complex number
solutions are usually introduced. The most
difficult application problem encountered are
typified by:
You are the manager of a clothing store and have just
purchased 100 dress shirts for $20.00 each. After 1 month of
selling the shirts at the regular price, you plan to have a sale
giving 40% off the original selling price. However, you still
want to make a profit of $4 on each shirt at the sale price.
What should you price the shirts at initially to ensure this?
If, instead of 40% off at the sale, you give 50% off, by how
much is your profit reduced?
A varies jointly as b & h. If A = 120, when b =
6 and h = 5, find A when b = 12 and h = 10.
(Sullivan 105)
A 62’ wire that makes an angle of 60 degrees
with the ground is attached to a telephone
pole. Find the distance from the base of the
pole to the point on the pole where the wire is
attached. Express your answer to the nearest
10th of a foot.
A truck firm wants to purchase a maximum of 15 new trucks
that will provide at least 36 tons of additional shipping
capacity. Model A truck holds 2 tons and costs $15,000 and
model B truck holds 3 tons and costs $24,000. How many
trucks of each model should the company purchase to
provide the additional shipping capacity at the minimum
cost? What is the minimum cost?
A review of the basic techniques is covered.
All topics are extended and they also involve
absolute value, quadratic and rational
inequalities. Occasionally linear inequalities
in two variables are covered. Interval notation
is usually introduced. The graphing calculator
is often used to aid in finding the solutions.
These problems may be the ones that students
find the most difficult, because they combine
many separate skills into one multi-step
problem. They require perhaps the greatest
amount of synthesis of any problem requiring
only manipulative skills. The most difficult
problems encountered are typified by:
1
In your Economics 101 class, you have scores of 68, 82, 87,
and 89 on the first four of five tests. To get a grade of B, the
average of the first five test scores must be greater than or
equal to 80 and less than 90. Solve an inequality to find the
range of the score that you need on the last test to get a B.
(Sullivan 135)
Solve the following inequalities, expressing
your answer in interval notation.
(x + 2)(x – 7) < 0
x2 + 2x – 7 > 0
|7x – 6| < 22
1
2

x  2 3x  9
C10
2
3,5
Safety Research: If a person driving a vehicle slams on the
brakes and skids to a stop, the speed v in miles per hour of
the vehicle at the same time the brakes are applied is given
approximately by v=f(x)=C=√x where x is the length in feet
of the skid marks and C is a constant that depends on the
road conditions and the weight of the vehicle. On the same
set of axis, graph v=f(x), 0<=x<=100, for C=3,4, and 5.
What has been covered in introductory algebra
is reviewed, and the techniques for solving
equations containing radicals are furthered by
investigating some more complicated
situations. Typical problems:
2x  3  7  x  2
x 1  2  x  2
Solve: √(3x2)=8 √(2x)-4√2
Solve for w: T  2
1
A 5 horsepower (hp) pump can empty a pool in 5 hours. A
smaller, 2 hp pump empties the same pool in 8 hours. The
pumps are used together to begin emptying this pool. After
two hours, the 2 hp pump breaks down. How long will it
take the larger pump to empty the pool?
(Sullivan, 105)
w
.
40
This topic is usually reviewed in Intermediate
Algebra as part of a general review to solving
equations that usually includes linear,
quadratic and rational equations together.
Further synthesis may be stressed by
investigating what happens as n  0 in the
equation n5  21  9n . Typical examples:
x
2
2
 
x2 3 x4
3,5
Solve algebraically and graphically:
|2x – 3| = |x + 5|
|5 – 6x| ≤ 10 + 7x
A much fuller discussion of absolute value
equations and inequalities are dealt with here
on this level. This Distance from 0 idea is
usually the major application. Typical
examples:
|2x + 1| > 1
(Keedy and Bittinger, 233)
|x + 4|<0
1
Katy, Mike, Danny, and Colleen agreed to do yard work at
home for $45 to be split among them. After they finished,
their father determined that Mike deserves twice what Katy
gets, Katy and Colleen deserve the same amount, and Danny
deserves half of what Katy gets. How much does each one
receive?
Usually the basic techniques are reviews and
then expanded to 3 x 3 systems. Some
intermediate algebra courses use linear algebra
(matrices and determinants) approaches to
solutions. Typical example:
Solve by any method:
2 x  y  3x  10
(Sullivan 896)
x  2 y  3z  2
3x  2 y  5z  16
Solve each equation:
3,5
1n  x  1  1n x  2
3,5
e x  e x
2
2
Exponential equations are often introduced in
Intermediate Algebra. Logs are used to find
solutions for variables that are in the exponent
of an exponential equation. In most
application problems the exponential equation
is explicitly given. The hardest application
problems are typified by:
The annual profit P of a company due to the
sales of a particular item after it has been on
C11
the market for x years is determined to be
P = $100,000 - $60,000 (½)x
3,5
6
6
a. What is the profit after 5 years? (10
years?)
b. When will the profit be $80,000?
c. What is the most profit that the company
can expect from this product?
Manipulative Skills not Implied by the Previous Topics
Intermediate Algebra
Write the expression as a single quotient in which only a
Facility with exponents is assumed of
positive exponent and/or radical appears:
students entering Intermediate Algebra, so
this topic is usually reviewed as it is needed
(x² + 4)½ - x²(x² + 4)-½
in other problems. If negative exponents are
x² + 4
not covered in Introductory Algebra, they are
covered here. Problems tend to be more
complex and rational exponents are usually
(Sullivan 78)
included. The complexity of the problems is
typified by:
Expand: (u – v)5.
(Keedy and Bittinger 721)
[9x²y1/3]½
x1/3y
th
6
1
1
Find the 8 term in the expansion of (2x – 5y) .
(2 x  5) 3 (2 x  5)  2
0
(Keedy and Bittinger 723)
 34
(2 x  5)
6
4
At one point in a recent season, Darryl Strawberry of the Los
Angeles Dodgers had a batting average of 0.313. Suppose he
came to bat 5 times in a game. The probability of his getting
exactly 3 hits is the 3rd term of the binomial expansion of
(0.313 + 0.687)5. Find that term and use your calculator to
estimate the probability.
(Keedy and Bittingeer 725)
Find the horizontal and oblique asymptotes to
H(x) = x4 + 2x² + 1
x² - x + 1.
In Intermediate Algebra polynomial long
division is often reviewed as part of a more
complex task, such as finding oblique
asymptotes for rational functions. Typical
example:
(Sullivan 327)
Find the horizontal and oblique asymptotes
1,4
Build a table and graph: f(x) = 1
x2
to H ( x ) 
x
f(x)
(Keedy and Bittinger 271)
4
Determine the vertical asymptote and explain your reasoning
3x – 2____
x(x – 5)(x + 3)
(Keedy and Bittinger 273
f(x) =
C12
3x 4  x 2
x3  x2  1
.
2,3
Given
3x – 2____
x(x – 5)(x +3)
a. Determine the vertical, horizontal and oblique
asymptotes, if they exist.
b. Explain the reasons for your response to (a).
c. Sketch a graph and illustrate the asymptote(s).
2
(Keedy/Bittinger, 273)
Find the complex zeros of each polynomial function and
write f in factored form.
f  x   x4 1
(Sullivan 386)
f  x   4 x3  4 x 2  7 x  2
(Sullivan 389)
Solve the equation: x 2  3  x
(Sullivan 389)
2,3
Show graphically 2 + 2i and 3 – i. Show also their sum.
(Keedy/Bittinger, 543)
2
Find |3 + 4i|
(Keedy/Bittinger, 544)
3
Find i29
(Keedy/Bittinger, 91)
C13
Factoring of trinomials is usually assumed of
students entering Intermediate Algebra. It is
usually reviewed in the context of other
problems, such as, solving quadratic
equations.