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  1. Preface
  2. 1 Foundations
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Use the Language of Algebra
    4. 1.3 Add and Subtract Integers
    5. 1.4 Multiply and Divide Integers
    6. 1.5 Visualize Fractions
    7. 1.6 Add and Subtract Fractions
    8. 1.7 Decimals
    9. 1.8 The Real Numbers
    10. 1.9 Properties of Real Numbers
    11. 1.10 Systems of Measurement
    12. Key Terms
    13. Key Concepts
    14. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Solving Linear Equations and Inequalities
    1. Introduction
    2. 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 2.2 Solve Equations using the Division and Multiplication Properties of Equality
    4. 2.3 Solve Equations with Variables and Constants on Both Sides
    5. 2.4 Use a General Strategy to Solve Linear Equations
    6. 2.5 Solve Equations with Fractions or Decimals
    7. 2.6 Solve a Formula for a Specific Variable
    8. 2.7 Solve Linear Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Math Models
    1. Introduction
    2. 3.1 Use a Problem-Solving Strategy
    3. 3.2 Solve Percent Applications
    4. 3.3 Solve Mixture Applications
    5. 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
    6. 3.5 Solve Uniform Motion Applications
    7. 3.6 Solve Applications with Linear Inequalities
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Graphs
    1. Introduction
    2. 4.1 Use the Rectangular Coordinate System
    3. 4.2 Graph Linear Equations in Two Variables
    4. 4.3 Graph with Intercepts
    5. 4.4 Understand Slope of a Line
    6. 4.5 Use the Slope-Intercept Form of an Equation of a Line
    7. 4.6 Find the Equation of a Line
    8. 4.7 Graphs of Linear Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Systems of Linear Equations
    1. Introduction
    2. 5.1 Solve Systems of Equations by Graphing
    3. 5.2 Solving Systems of Equations by Substitution
    4. 5.3 Solve Systems of Equations by Elimination
    5. 5.4 Solve Applications with Systems of Equations
    6. 5.5 Solve Mixture Applications with Systems of Equations
    7. 5.6 Graphing Systems of Linear Inequalities
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Polynomials
    1. Introduction
    2. 6.1 Add and Subtract Polynomials
    3. 6.2 Use Multiplication Properties of Exponents
    4. 6.3 Multiply Polynomials
    5. 6.4 Special Products
    6. 6.5 Divide Monomials
    7. 6.6 Divide Polynomials
    8. 6.7 Integer Exponents and Scientific Notation
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Factoring
    1. Introduction
    2. 7.1 Greatest Common Factor and Factor by Grouping
    3. 7.2 Factor Trinomials of the Form x2+bx+c
    4. 7.3 Factor Trinomials of the Form ax2+bx+c
    5. 7.4 Factor Special Products
    6. 7.5 General Strategy for Factoring Polynomials
    7. 7.6 Quadratic Equations
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Rational Expressions and Equations
    1. Introduction
    2. 8.1 Simplify Rational Expressions
    3. 8.2 Multiply and Divide Rational Expressions
    4. 8.3 Add and Subtract Rational Expressions with a Common Denominator
    5. 8.4 Add and Subtract Rational Expressions with Unlike Denominators
    6. 8.5 Simplify Complex Rational Expressions
    7. 8.6 Solve Rational Equations
    8. 8.7 Solve Proportion and Similar Figure Applications
    9. 8.8 Solve Uniform Motion and Work Applications
    10. 8.9 Use Direct and Inverse Variation
    11. Key Terms
    12. Key Concepts
    13. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Roots and Radicals
    1. Introduction
    2. 9.1 Simplify and Use Square Roots
    3. 9.2 Simplify Square Roots
    4. 9.3 Add and Subtract Square Roots
    5. 9.4 Multiply Square Roots
    6. 9.5 Divide Square Roots
    7. 9.6 Solve Equations with Square Roots
    8. 9.7 Higher Roots
    9. 9.8 Rational Exponents
    10. Key Terms
    11. Key Concepts
    12. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Quadratic Equations
    1. Introduction
    2. 10.1 Solve Quadratic Equations Using the Square Root Property
    3. 10.2 Solve Quadratic Equations by Completing the Square
    4. 10.3 Solve Quadratic Equations Using the Quadratic Formula
    5. 10.4 Solve Applications Modeled by Quadratic Equations
    6. 10.5 Graphing Quadratic Equations in Two Variables
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  12. 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
  13. Index

6.1 Add and Subtract Polynomials

  • Monomials
    • A monomial is a term of the form axmaxm, where aa is a constant and mm is a whole number
  • Polynomials
    • polynomial—A monomial, or two or more monomials combined by addition or subtraction is a polynomial.
    • monomial—A polynomial with exactly one term is called a monomial.
    • binomial—A polynomial with exactly two terms is called a binomial.
    • trinomial—A polynomial with exactly three terms is called a trinomial.
  • Degree of a Polynomial
    • The degree of a term is the sum of the exponents of its variables.
    • The degree of a constant is 0.
    • The degree of a polynomial is the highest degree of all its terms.

6.2 Use Multiplication Properties of Exponents

  • Exponential Notation
    This figure has two columns. In the left column is a to the m power. The m is labeled in blue as an exponent. The a is labeled in red as the base. In the right column is the text “a to the m powder means multiply m factors of a.” Below this is a to the m power equals a times a times a times a, followed by an ellipsis, with “m factors” written below in blue.
  • Properties of Exponents
    • If a,ba,b are real numbers and m,nm,n are whole numbers, then
      Product Propertyam·an=am+nPower Property(am)n=am·nProduct to a Power(ab)m=ambmProduct Propertyam·an=am+nPower Property(am)n=am·nProduct to a Power(ab)m=ambm

6.3 Multiply Polynomials

  • FOIL Method for Multiplying Two Binomials—To multiply two binomials:
    1. Step 1. Multiply the First terms.
    2. Step 2. Multiply the Outer terms.
    3. Step 3. Multiply the Inner terms.
    4. Step 4. Multiply the Last terms.

  • Multiplying Two Binomials—To multiply binomials, use the:
  • Multiplying a Trinomial by a Binomial—To multiply a trinomial by a binomial, use the:

6.4 Special Products

  • Binomial Squares Pattern
    • If a,ba,b are real numbers,
      No Alt Text
    • (a+b)2=a2+2ab+b2(a+b)2=a2+2ab+b2
    • (ab)2=a22ab+b2(ab)2=a22ab+b2
    • To square a binomial: square the first term, square the last term, double their product.

  • Product of Conjugates Pattern
    • If a,ba,b are real numbers,
      No Alt Text
    • (ab)(a+b)=a2b2(ab)(a+b)=a2b2
    • The product is called a difference of squares.

  • To multiply conjugates:
    • square the first term square the last term write it as a difference of squares

6.5 Divide Monomials

  • Quotient Property for Exponents:
    • If aa is a real number, a0a0, and m,nm,n are whole numbers, then:
      aman=amn,m>nandaman=1amn,n>maman=amn,m>nandaman=1amn,n>m
  • Zero Exponent
    • If aa is a non-zero number, then a0=1a0=1.

  • Quotient to a Power Property for Exponents:
    • If aa and bb are real numbers, b0,b0, and mm is a counting number, then:
      (ab)m=ambm(ab)m=ambm
    • To raise a fraction to a power, raise the numerator and denominator to that power.

  • Summary of Exponent Properties
    • If a,ba,b are real numbers and m,nm,n are whole numbers, then
      Product Propertyam·an=am+nPower Property(am)n=am·nProduct to a Power(ab)m=ambmQuotient Propertyambm=amn,a0,m>naman=1anm,a0,n>mZero Exponent Definitionao=1,a0Quotient to a Power Property(ab)m=ambm,b0Product Propertyam·an=am+nPower Property(am)n=am·nProduct to a Power(ab)m=ambmQuotient Propertyambm=amn,a0,m>naman=1anm,a0,n>mZero Exponent Definitionao=1,a0Quotient to a Power Property(ab)m=ambm,b0

6.6 Divide Polynomials

  • Fraction Addition
    • If a,b,andca,b,andc are numbers where c0c0, then
      ac+bc=a+bcanda+bc=ac+bcac+bc=a+bcanda+bc=ac+bc

  • Division of a Polynomial by a Monomial
    • To divide a polynomial by a monomial, divide each term of the polynomial by the monomial.

6.7 Integer Exponents and Scientific Notation

  • Property of Negative Exponents
    • If nn is a positive integer and a0a0, then 1an=an1an=an
  • Quotient to a Negative Exponent
    • If a,ba,b are real numbers, b0b0 and nn is an integer , then (ab)n=(ba)n(ab)n=(ba)n
  • To convert a decimal to scientific notation:
    1. Step 1. Move the decimal point so that the first factor is greater than or equal to 1 but less than 10.
    2. Step 2. Count the number of decimal places, nn, that the decimal point was moved.
    3. Step 3. Write the number as a product with a power of 10. If the original number is:
      • greater than 1, the power of 10 will be 10n10n
      • between 0 and 1, the power of 10 will be 10n10n
    4. Step 4. Check.

  • To convert scientific notation to decimal form:
    1. Step 1. Determine the exponent, nn, on the factor 10.
    2. Step 2. Move the decimal nnplaces, adding zeros if needed.
      • If the exponent is positive, move the decimal point nn places to the right.
      • If the exponent is negative, move the decimal point |n||n| places to the left.
    3. Step 3. Check.
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