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Intermediate Algebra 2e

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Intermediate Algebra 2eIndex
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Table of contents
  1. Preface
  2. 1 Foundations
    1. Introduction
    2. 1.1 Use the Language of Algebra
    3. 1.2 Integers
    4. 1.3 Fractions
    5. 1.4 Decimals
    6. 1.5 Properties of Real Numbers
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Solving Linear Equations
    1. Introduction
    2. 2.1 Use a General Strategy to Solve Linear Equations
    3. 2.2 Use a Problem Solving Strategy
    4. 2.3 Solve a Formula for a Specific Variable
    5. 2.4 Solve Mixture and Uniform Motion Applications
    6. 2.5 Solve Linear Inequalities
    7. 2.6 Solve Compound Inequalities
    8. 2.7 Solve Absolute Value Inequalities
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Graphs and Functions
    1. Introduction
    2. 3.1 Graph Linear Equations in Two Variables
    3. 3.2 Slope of a Line
    4. 3.3 Find the Equation of a Line
    5. 3.4 Graph Linear Inequalities in Two Variables
    6. 3.5 Relations and Functions
    7. 3.6 Graphs of Functions
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Systems of Linear Equations
    1. Introduction
    2. 4.1 Solve Systems of Linear Equations with Two Variables
    3. 4.2 Solve Applications with Systems of Equations
    4. 4.3 Solve Mixture Applications with Systems of Equations
    5. 4.4 Solve Systems of Equations with Three Variables
    6. 4.5 Solve Systems of Equations Using Matrices
    7. 4.6 Solve Systems of Equations Using Determinants
    8. 4.7 Graphing Systems of Linear Inequalities
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Polynomials and Polynomial Functions
    1. Introduction
    2. 5.1 Add and Subtract Polynomials
    3. 5.2 Properties of Exponents and Scientific Notation
    4. 5.3 Multiply Polynomials
    5. 5.4 Dividing Polynomials
    6. Chapter Review
      1. Key Terms
      2. Key Concepts
    7. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Factoring
    1. Introduction to Factoring
    2. 6.1 Greatest Common Factor and Factor by Grouping
    3. 6.2 Factor Trinomials
    4. 6.3 Factor Special Products
    5. 6.4 General Strategy for Factoring Polynomials
    6. 6.5 Polynomial Equations
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Rational Expressions and Functions
    1. Introduction
    2. 7.1 Multiply and Divide Rational Expressions
    3. 7.2 Add and Subtract Rational Expressions
    4. 7.3 Simplify Complex Rational Expressions
    5. 7.4 Solve Rational Equations
    6. 7.5 Solve Applications with Rational Equations
    7. 7.6 Solve Rational Inequalities
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Roots and Radicals
    1. Introduction
    2. 8.1 Simplify Expressions with Roots
    3. 8.2 Simplify Radical Expressions
    4. 8.3 Simplify Rational Exponents
    5. 8.4 Add, Subtract, and Multiply Radical Expressions
    6. 8.5 Divide Radical Expressions
    7. 8.6 Solve Radical Equations
    8. 8.7 Use Radicals in Functions
    9. 8.8 Use the Complex Number System
    10. Chapter Review
      1. Key Terms
      2. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Quadratic Equations and Functions
    1. Introduction
    2. 9.1 Solve Quadratic Equations Using the Square Root Property
    3. 9.2 Solve Quadratic Equations by Completing the Square
    4. 9.3 Solve Quadratic Equations Using the Quadratic Formula
    5. 9.4 Solve Equations in Quadratic Form
    6. 9.5 Solve Applications of Quadratic Equations
    7. 9.6 Graph Quadratic Functions Using Properties
    8. 9.7 Graph Quadratic Functions Using Transformations
    9. 9.8 Solve Quadratic Inequalities
    10. Chapter Review
      1. Key Terms
      2. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Exponential and Logarithmic Functions
    1. Introduction
    2. 10.1 Finding Composite and Inverse Functions
    3. 10.2 Evaluate and Graph Exponential Functions
    4. 10.3 Evaluate and Graph Logarithmic Functions
    5. 10.4 Use the Properties of Logarithms
    6. 10.5 Solve Exponential and Logarithmic Equations
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  12. 11 Conics
    1. Introduction
    2. 11.1 Distance and Midpoint Formulas; Circles
    3. 11.2 Parabolas
    4. 11.3 Ellipses
    5. 11.4 Hyperbolas
    6. 11.5 Solve Systems of Nonlinear Equations
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  13. 12 Sequences, Series and Binomial Theorem
    1. Introduction
    2. 12.1 Sequences
    3. 12.2 Arithmetic Sequences
    4. 12.3 Geometric Sequences and Series
    5. 12.4 Binomial Theorem
    6. Chapter Review
      1. Key Terms
      2. Key Concepts
    7. Exercises
      1. Review Exercises
      2. Practice Test
  14. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
  15. Index
A
absolute value 1.2 Integers, 2.7 Solve Absolute Value Inequalities, 8.1 Simplify Expressions with Roots
absolute value equation 2.7 Solve Absolute Value Inequalities
absolute value inequality 2.7 Solve Absolute Value Inequalities
additive identity 1.5 Properties of Real Numbers
additive inverse 1.5 Properties of Real Numbers
amount of discount 2.2 Use a Problem Solving Strategy
annuity 12.3 Geometric Sequences and Series
area 2.3 Solve a Formula for a Specific Variable
arithmetic sequence 12.2 Arithmetic Sequences
Associative Property 1.5 Properties of Real Numbers
asymptote 10.2 Evaluate and Graph Exponential Functions
augmented matrix 4.5 Solve Systems of Equations Using Matrices
axis of symmetry 9.6 Graph Quadratic Functions Using Properties, 9.7 Graph Quadratic Functions Using Transformations
B
base 1.1 Use the Language of Algebra
binomial coefficient 12.4 Binomial Theorem
Binomial Theorem 12.4 Binomial Theorem, 12.4 Binomial Theorem
boundary line 3.4 Graph Linear Inequalities in Two Variables
break-even point 4.3 Solve Mixture Applications with Systems of Equations
C
Change-of-Base Formula 10.4 Use the Properties of Logarithms
circle 11.1 Distance and Midpoint Formulas; Circles, 11.1 Distance and Midpoint Formulas; Circles, 11.1 Distance and Midpoint Formulas; Circles, 11.1 Distance and Midpoint Formulas; Circles
coefficient 1.1 Use the Language of Algebra, 2.1 Use a General Strategy to Solve Linear Equations
coincident 4.1 Solve Systems of Linear Equations with Two Variables
common difference 12.2 Arithmetic Sequences
common logarithmic function 10.3 Evaluate and Graph Logarithmic Functions
common ratio 12.3 Geometric Sequences and Series
Commutative Property 1.5 Properties of Real Numbers
complementary angles 4.2 Solve Applications with Systems of Equations
completing the square 9.2 Solve Quadratic Equations by Completing the Square, 9.2 Solve Quadratic Equations by Completing the Square, 9.2 Solve Quadratic Equations by Completing the Square
complex conjugate pair 8.8 Use the Complex Number System
complex fraction 1.3 Fractions
complex number 8.8 Use the Complex Number System
complex number system 8.8 Use the Complex Number System
complex rational expression 7.3 Simplify Complex Rational Expressions
composition 10.1 Finding Composite and Inverse Functions, 10.4 Use the Properties of Logarithms
compound inequality 2.6 Solve Compound Inequalities, 2.6 Solve Compound Inequalities, 2.6 Solve Compound Inequalities
compound interest 10.2 Evaluate and Graph Exponential Functions
conditional equation 2.1 Use a General Strategy to Solve Linear Equations
conjugate pair 5.3 Multiply Polynomials
consecutive even integers 2.2 Use a Problem Solving Strategy
consecutive integers 2.2 Use a Problem Solving Strategy
consecutive odd integers 2.2 Use a Problem Solving Strategy
consistent system of equations 4.1 Solve Systems of Linear Equations with Two Variables
constant 1.1 Use the Language of Algebra
contradiction 2.1 Use a General Strategy to Solve Linear Equations
cost function 4.3 Solve Mixture Applications with Systems of Equations
critical point 7.6 Solve Rational Inequalities
critical points 9.8 Solve Quadratic Inequalities
D
degree of a constant 5.1 Add and Subtract Polynomials
degree of a polynomial 5.1 Add and Subtract Polynomials
degree of the polynomial equation 6.5 Polynomial Equations
degree one 6.5 Polynomial Equations
degree two 6.5 Polynomial Equations
denominator 1.3 Fractions
determinant 4.6 Solve Systems of Equations Using Determinants
difference of squares 8.8 Use the Complex Number System
discount rate 2.2 Use a Problem Solving Strategy
discriminant 9.3 Solve Quadratic Equations Using the Quadratic Formula, 9.6 Graph Quadratic Functions Using Properties
Distributive Property 1.5 Properties of Real Numbers, 8.4 Add, Subtract, and Multiply Radical Expressions, 8.8 Use the Complex Number System
divisible 1.1 Use the Language of Algebra
domain 3.5 Relations and Functions, 8.7 Use Radicals in Functions, 8.7 Use Radicals in Functions
double inequality 2.6 Solve Compound Inequalities
E
earthquake intensity 10.3 Evaluate and Graph Logarithmic Functions
ellipse 11.1 Distance and Midpoint Formulas; Circles, 11.3 Ellipses, 11.3 Ellipses, 11.3 Ellipses
equal 1.1 Use the Language of Algebra
equal sign 2.1 Use a General Strategy to Solve Linear Equations
equation 1.1 Use the Language of Algebra
equivalent fractions 1.3 Fractions
evaluate an expression 1.1 Use the Language of Algebra
exponent 1.1 Use the Language of Algebra
exponential decay 10.2 Evaluate and Graph Exponential Functions, 10.5 Solve Exponential and Logarithmic Equations
exponential function 10.2 Evaluate and Graph Exponential Functions
exponential growth 10.2 Evaluate and Graph Exponential Functions
expression 1.1 Use the Language of Algebra
extraneous solution 8.6 Solve Radical Equations
extraneous solution to a rational equation 7.4 Solve Rational Equations
F
factorial notation 12.1 Sequences, 12.4 Binomial Theorem
factoring 6.1 Greatest Common Factor and Factor by Grouping
factoring by substitution 6.2 Factor Trinomials
factors 1.1 Use the Language of Algebra, 1.1 Use the Language of Algebra
finite sequence 12.1 Sequences
FOIL 6.2 Factor Trinomials, 6.2 Factor Trinomials, 8.8 Use the Complex Number System
fraction 1.3 Fractions
function 3.5 Relations and Functions, 10.1 Finding Composite and Inverse Functions
G
GCF 6.1 Greatest Common Factor and Factor by Grouping, 6.2 Factor Trinomials, 6.3 Factor Special Products
General Strategy for Solving Linear Equations 2.1 Use a General Strategy to Solve Linear Equations, 2.1 Use a General Strategy to Solve Linear Equations
general term 12.1 Sequences
geometric sequence 12.3 Geometric Sequences and Series
gravity 8.6 Solve Radical Equations
greatest common factor 6.1 Greatest Common Factor and Factor by Grouping
grouping symbols 8.1 Simplify Expressions with Roots
H
half-life 10.5 Solve Exponential and Logarithmic Equations
horizontal line 3.1 Graph Linear Equations in Two Variables
horizontal line test 10.1 Finding Composite and Inverse Functions
hyperbola 11.1 Distance and Midpoint Formulas; Circles, 11.4 Hyperbolas
I
identity 2.1 Use a General Strategy to Solve Linear Equations
Identity Property of Addition 1.5 Properties of Real Numbers
Identity Property of Multiplication 1.5 Properties of Real Numbers
imaginary unit 8.8 Use the Complex Number System
inconsistent system of equations 4.1 Solve Systems of Linear Equations with Two Variables
infinite geometric series 12.3 Geometric Sequences and Series
infinite sequence 12.1 Sequences
integers 1.2 Integers
intercepts of a line 3.1 Graph Linear Equations in Two Variables
interest 2.2 Use a Problem Solving Strategy
interval notation 2.6 Solve Compound Inequalities
inverse function 10.1 Finding Composite and Inverse Functions
Inverse Property of Addition 1.5 Properties of Real Numbers
Inverse Property of Multiplication 1.5 Properties of Real Numbers
irrational number 1.4 Decimals
L
leading coefficient 9.2 Solve Quadratic Equations by Completing the Square
least common denominator 1.3 Fractions, 2.1 Use a General Strategy to Solve Linear Equations, 2.1 Use a General Strategy to Solve Linear Equations
least common multiple 1.1 Use the Language of Algebra
like radicals 8.4 Add, Subtract, and Multiply Radical Expressions
like terms 1.1 Use the Language of Algebra
linear equation 2.1 Use a General Strategy to Solve Linear Equations, 3.1 Graph Linear Equations in Two Variables, 4.4 Solve Systems of Equations with Three Variables
linear inequality 3.4 Graph Linear Inequalities in Two Variables
list price 2.2 Use a Problem Solving Strategy
M
mapping 3.5 Relations and Functions
mark-up 2.2 Use a Problem Solving Strategy
matrix 4.5 Solve Systems of Equations Using Matrices
maximum 9.6 Graph Quadratic Functions Using Properties
minimum 9.6 Graph Quadratic Functions Using Properties
minor of an entry 4.6 Solve Systems of Equations Using Determinants
monomial 5.1 Add and Subtract Polynomials
multiple 1.1 Use the Language of Algebra
multiplicative identity 1.5 Properties of Real Numbers
multiplicative inverse 1.5 Properties of Real Numbers
N
natural base 10.2 Evaluate and Graph Exponential Functions
natural exponential function 10.2 Evaluate and Graph Exponential Functions
natural logarithmic function 10.3 Evaluate and Graph Logarithmic Functions
negative number 1.2 Integers
number line 1.1 Use the Language of Algebra
numerator 1.3 Fractions
O
one-to-one 10.1 Finding Composite and Inverse Functions
One-to-One Property of Logarithmic Equations 10.5 Solve Exponential and Logarithmic Equations
opposite 1.2 Integers
order of operations 1.1 Use the Language of Algebra, 8.2 Simplify Radical Expressions
ordered pair 3.1 Graph Linear Equations in Two Variables
ordered triple 4.4 Solve Systems of Equations with Three Variables
origin 3.1 Graph Linear Equations in Two Variables
original cost 2.2 Use a Problem Solving Strategy
P
parabola 9.6 Graph Quadratic Functions Using Properties, 11.1 Distance and Midpoint Formulas; Circles, 11.2 Parabolas, 11.2 Parabolas, 11.2 Parabolas
parallel lines 3.2 Slope of a Line
partial sum 12.1 Sequences
Pascal’s Triangle 12.4 Binomial Theorem, 12.4 Binomial Theorem
percent 1.4 Decimals
percent change 2.2 Use a Problem Solving Strategy
perfect square 6.3 Factor Special Products, 8.1 Simplify Expressions with Roots
perimeter 2.3 Solve a Formula for a Specific Variable, 2.3 Solve a Formula for a Specific Variable
perpendicular lines 3.2 Slope of a Line
point-slope form 3.3 Find the Equation of a Line
polynomial 5.1 Add and Subtract Polynomials, 6.1 Greatest Common Factor and Factor by Grouping
polynomial equation 6.5 Polynomial Equations
polynomial function 5.1 Add and Subtract Polynomials
Power Property 5.2 Properties of Exponents and Scientific Notation, 8.3 Simplify Rational Exponents
Power Property for Exponents 8.3 Simplify Rational Exponents
Power Property of Logarithms 10.4 Use the Properties of Logarithms
prime 6.1 Greatest Common Factor and Factor by Grouping, 6.2 Factor Trinomials, 6.3 Factor Special Products, 6.4 General Strategy for Factoring Polynomials
prime factorization 1.1 Use the Language of Algebra
prime number 1.1 Use the Language of Algebra
principal 2.2 Use a Problem Solving Strategy
principal square root 1.4 Decimals, 8.1 Simplify Expressions with Roots
product 6.1 Greatest Common Factor and Factor by Grouping
Product of Binomial Squares Pattern 8.4 Add, Subtract, and Multiply Radical Expressions, 8.8 Use the Complex Number System
Product of Conjugates Pattern 8.5 Divide Radical Expressions, 8.8 Use the Complex Number System
Product Property 5.2 Properties of Exponents and Scientific Notation, 5.2 Properties of Exponents and Scientific Notation, 8.3 Simplify Rational Exponents
Product Property of Logarithms 10.4 Use the Properties of Logarithms
Product Property of Roots 8.2 Simplify Radical Expressions, 8.4 Add, Subtract, and Multiply Radical Expressions
Product to a Power 5.2 Properties of Exponents and Scientific Notation
Product to a Power Property 8.3 Simplify Rational Exponents
Properties of Exponents 5.2 Properties of Exponents and Scientific Notation
Properties of Negative Exponents 5.2 Properties of Exponents and Scientific Notation
proportion 7.5 Solve Applications with Rational Equations
Pythagorean Theorem 2.3 Solve a Formula for a Specific Variable, 9.5 Solve Applications of Quadratic Equations
Q
quadratic equation 6.5 Polynomial Equations, 6.5 Polynomial Equations, 6.5 Polynomial Equations, 9.1 Solve Quadratic Equations Using the Square Root Property, 9.2 Solve Quadratic Equations by Completing the Square, 9.2 Solve Quadratic Equations by Completing the Square, 9.3 Solve Quadratic Equations Using the Quadratic Formula, 9.8 Solve Quadratic Inequalities
quadratic form 9.4 Solve Equations in Quadratic Form
Quadratic Formula 9.3 Solve Quadratic Equations Using the Quadratic Formula, 9.3 Solve Quadratic Equations Using the Quadratic Formula, 9.3 Solve Quadratic Equations Using the Quadratic Formula, 9.5 Solve Applications of Quadratic Equations, 9.6 Graph Quadratic Functions Using Properties
quadratic function 9.6 Graph Quadratic Functions Using Properties
quadratic inequality 9.8 Solve Quadratic Inequalities
Quotient Property 5.2 Properties of Exponents and Scientific Notation, 5.2 Properties of Exponents and Scientific Notation, 8.2 Simplify Radical Expressions, 8.2 Simplify Radical Expressions, 8.3 Simplify Rational Exponents
Quotient Property of Logarithms 10.4 Use the Properties of Logarithms
Quotient Property of Radical Expressions 8.5 Divide Radical Expressions
Quotient to a Negative Power 5.2 Properties of Exponents and Scientific Notation
Quotient to a Power Property 5.2 Properties of Exponents and Scientific Notation, 8.2 Simplify Radical Expressions
R
radical 9.3 Solve Quadratic Equations Using the Quadratic Formula
radical equation 8.6 Solve Radical Equations
radical expression 8.2 Simplify Radical Expressions, 8.5 Divide Radical Expressions
radical function 8.7 Use Radicals in Functions
radicand 9.3 Solve Quadratic Equations Using the Quadratic Formula
range 8.7 Use Radicals in Functions
rate of interest 2.2 Use a Problem Solving Strategy
rational equation 7.4 Solve Rational Equations
rational expression 7.1 Multiply and Divide Rational Expressions, 7.1 Multiply and Divide Rational Expressions
rational function 7.1 Multiply and Divide Rational Expressions
rational inequality 7.6 Solve Rational Inequalities
rational number 1.4 Decimals
rationalize the denominator 8.5 Divide Radical Expressions, 9.1 Solve Quadratic Equations Using the Square Root Property
rationalizing the denominator 8.5 Divide Radical Expressions
real number 1.4 Decimals
reciprocal 1.3 Fractions
relation 3.5 Relations and Functions
revenue 4.3 Solve Mixture Applications with Systems of Equations
right triangle 2.3 Solve a Formula for a Specific Variable
row-echelon form 4.5 Solve Systems of Equations Using Matrices
S
scientific notation 5.2 Properties of Exponents and Scientific Notation
sequence 12.1 Sequences
similar figures 7.5 Solve Applications with Rational Equations
simple interest 2.2 Use a Problem Solving Strategy
simplified rational expression 7.1 Multiply and Divide Rational Expressions
simplify an expression 1.1 Use the Language of Algebra
solution 2.1 Use a General Strategy to Solve Linear Equations, 3.1 Graph Linear Equations in Two Variables
solution to a linear inequality 3.4 Graph Linear Inequalities in Two Variables
solutions of a system of equations 4.1 Solve Systems of Linear Equations with Two Variables
solutions of the system of three linear equations with three variables 4.4 Solve Systems of Equations with Three Variables
speed 8.6 Solve Radical Equations
square 8.1 Simplify Expressions with Roots
square matrix 4.6 Solve Systems of Equations Using Determinants
square of a number 1.4 Decimals
square root 8.1 Simplify Expressions with Roots
square root of a number 1.4 Decimals
Square Root Property 9.1 Solve Quadratic Equations Using the Square Root Property, 9.1 Solve Quadratic Equations Using the Square Root Property, 9.1 Solve Quadratic Equations Using the Square Root Property, 9.2 Solve Quadratic Equations by Completing the Square, 9.2 Solve Quadratic Equations by Completing the Square
standard form 6.5 Polynomial Equations, 6.5 Polynomial Equations
standard form of a linear equation 3.1 Graph Linear Equations in Two Variables
standard form of a polynomial 5.1 Add and Subtract Polynomials
summation notation 12.1 Sequences
supplementary angles 4.2 Solve Applications with Systems of Equations
surface area 2.3 Solve a Formula for a Specific Variable
system of linear equations 4.1 Solve Systems of Linear Equations with Two Variables
system of linear inequalities 4.7 Graphing Systems of Linear Inequalities
system of nonlinear equations 11.5 Solve Systems of Nonlinear Equations
systems of equations 4.4 Solve Systems of Equations with Three Variables
T
temperature 2.3 Solve a Formula for a Specific Variable
term 1.1 Use the Language of Algebra
trinomial 5.1 Add and Subtract Polynomials, 6.2 Factor Trinomials, 6.3 Factor Special Products, 7.4 Solve Rational Equations, 9.3 Solve Quadratic Equations Using the Quadratic Formula
U
uniform motion 2.4 Solve Mixture and Uniform Motion Applications
union symbol 2.6 Solve Compound Inequalities
V
variable 1.1 Use the Language of Algebra, 2.1 Use a General Strategy to Solve Linear Equations
vertex 9.6 Graph Quadratic Functions Using Properties, 9.6 Graph Quadratic Functions Using Properties
vertical line 3.1 Graph Linear Equations in Two Variables
vertical line test 10.1 Finding Composite and Inverse Functions
volume 2.3 Solve a Formula for a Specific Variable
X
x-intercept 6.5 Polynomial Equations
Z
Zero Exponent Property 5.2 Properties of Exponents and Scientific Notation
zero of the function 6.5 Polynomial Equations
Zero Product Property 6.5 Polynomial Equations, 6.5 Polynomial Equations, 6.5 Polynomial Equations, 6.5 Polynomial Equations, 6.5 Polynomial Equations, 9.2 Solve Quadratic Equations by Completing the Square, 9.3 Solve Quadratic Equations Using the Quadratic Formula
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