Course Outline for DMA 060
POLYNOMIALS AND QUADRATIC APPLICATIONS
I.
CATALOG DESCRIPTION:
DMA 060 – Polynomials and Quadratic Applications - 1 credit (5 contact hours per week for four weeks or
2.5 hours per week for eight weeks)
This course provides a conceptual study of problems involving graphic and algebraic representations of
quadratics. Topics include basic polynomial operations, factoring polynomials, and solving polynomial
equations by means of factoring. Upon completion, students should be able to find algebraic solutions to
contextual problems with quadratic applications.
II.
PREREQUISITE: DMA 010, DMA 020. DMA 030, DMA 040 and DMA 050; or MAT 060, DMA 040 and
DMA 050; or MAT 060 and MAT 070
III.
COREQUISITE: None
IV.
EXPECTED STUDENT LEARNING OUTCOMES:
Upon completion of the course, students should be able to:
A.
B.
C.
D.
E.
F.
G.
H.
I.
Demonstrate the use of a problem solving strategy to include multiple representations of the
situation, organization of the information, and algebraic representation of quadratic equations.
Add and subtract polynomials.
Apply exponent rules.
Multiply polynomials.
Divide a polynomial by a monomial.
Factor trinomials using multiple methods.
Factor the difference of two squares.
Solve quadratic applications using the zero product property and critique the reasonableness of
solutions found.
Given the graph of a parabola, identify the vertex and x-intercepts.
V.
METHODS OF INSTRUCTION:
A.
Video lectures in basic concepts and skills
B.
Read text
C.
Class and group discussion of topics
D.
Skill-building computer exercises
VI.
CONTENT:
A.
Introduction to Polynomials: evaluate a polynomial for a given value of the variable, identify the
terms of a polynomial, identify the like terms of a polynomial, identify the coefficients of a
polynomial, identify the coefficients of a polynomial, collect the like terms of a polynomial, arrange a
polynomial in descending order, or collect the like terms and then arrange in descending order,
identify the degree of each of the terms of a polynomial and the degree of the polynomial, identify
the missing terms of a polynomial, classify a polynomial as a monomial, a binomial, a trinomial, or
none of these, evaluate a polynomial in several variables for given values of the variables, identify
the coefficients and the degrees of the terms of a polynomial and the degree of a polynomial in
several variables, collect like terms of a polynomial in several variables.
B.
C.
D.
Addition and Subtraction of Polynomials: add polynomials, simplify the opposite of a polynomial,
subtract polynomials, use polynomials to represent perimeter and area, add polynomials in several
variables, subtract polynomials in several variables.
Multiplication and Division of Polynomials: multiply monomials, multiply a monomial and any
polynomial, multiply two binomials, multiply any two polynomials, multiply two binomials mentally
using the FOIL method, multiply the sum and difference of two terms mentally, square a binomial
mentally, find special products when polynomial products are mixed together, multiply polynomials
in several variables, divide a polynomial by a monomial.
Introduction to Factoring: find the greatest common factor of a monomial, factor polynomials when
the terms have a common factor, factoring out the greatest common factor, factor certain
expressions with four terms using factoring by grouping.
x 2  bx  c : factor trinomials of this type by examining the
E.
Factoring Trinomials of the Type
constant term c.
F.
Factoring Trinomials of the Type ax  bx  c, a  1 : factor trinomials of this type using the FOIL
method, factor trinomials of this type using the ac-method.
Factoring Trinomial Squares and Differences of Squares: recognize trinomial squares, factor
trinomial squares, recognize differences of squares, factor differences of squares being careful to
factor completely.
Solving Quadratic Equations by Factoring: solve equations already factored using the principle of
zero products, solve quadratic equations by factoring and then using the principle of zero products,
solve applied problems involving quadratic equations that can be solved by factoring.
G.
H.
2
VII.
TYPICAL ASSIGNMENTS:
A.
In class participation
B.
Online or textbook homework
C.
Mid-module quizzes
D.
Online Post-module tests
VIII.
EVALUATION:
A.
Methods of Evaluation
1.
Students are evaluated online using module homework, mid-module quiz, module posttest.
B.
Frequency of Evaluation
1.
Each module will have several homework assignments, a mid-module quiz and a module
post-test.
IX.
TYPICAL TEXT:
Bittinger and Beecher, Mathematical Skills for Mastery. 1st Edition. Pearson, Addison Wesley Publishing.
X.
OTHER SUPPLIES REQUIRED OF STUDENTS:
A scientific calculator and a MyLabsPlus student access code are additional requirements for students. It
is highly recommended that students in all sections of the course have internet access.
Creation date: July 2, 2012
Modified by: Caroline Greenough; April 18, 2016