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MDTP Modules

  • LINR
    • Module 1
      • Lesson 1: Linear Patterns and Multiple Representations
      • Lesson 2: Graphs and Equations of Linear Situations
      • Lesson 3: Graphs in Slope-Intercept Form
      • Lesson 4: Writing the Equation of a Line
    • Module 2
      • Lesson 1: Solving Equations Including Absolute Value
      • Lesson 2: Solving Equations and Inequalities (Including Absolute Value)
      • Lesson 3: Linear Inequalities in Two Variables
    • Module 3
      • Lesson 1: Analyzing, writing, and solving linear systems
      • Lesson 2: Writing, solving, interpreting linear systems of inequalities
      • Lesson 3: Understanding and Using Absolute Value
      • Lesson 4: Solving Linear Systems with Geometric Applications
  • RATL
    • Module 1
      • Lesson 1: Operations on Fractions
      • Lesson 2: Using Percentages
      • Lesson 3: Multiplicative Thinking
      • Lesson 4: Proportional Reasoning
    • Module 2
      • Lesson 1: Introduction to Rational Expressions
      • Lesson 2: Adding and Subtracting Rational Expressions
      • Lesson 3: Multiplying and Dividing Rational Numbers
      • Lesson 4: Solving rational equations and writing rational equations from contextual situations
    • Module 3
      • Lesson 1: Evaluating Rational Expressions
      • Lesson 2: Solving Rational Inequalities
      • Lesson 3: Zeros and Asymptotes of Rational Functions
      • Lesson 4: Graphing Rational Functions
  • POLQ
    • Module 1
      • Lesson 1: Multiplication of Polynomials
      • Lesson 2: Division of Polynomials
      • Lesson 3: Factoring Polynomials
      • Lesson 4: Summative Polynomial Performance Task
    • Module 2
      • Lesson 1: Special Factoring Patterns
      • Lesson 2: Completing the square to solve quadratic equations
      • Lesson 3: Solving Radical Equations
      • Lesson 4: Deriving the quadratic formula
    • Module 3
      • Lesson 1: Introduction to Graphing Polynomials
      • Lesson 2: Roots of Polynomials and Polynomial Theorems
      • Lesson 3: Polynomials features: multiplicity, degree, end behavior
      • Lesson 4: Applications of Polynomials
  • GEOM
    • Module 1
      • Lesson 1: Developing formulas for area of multiple shapes
      • Lesson 2: Extending and Applying Area and Perimeter
      • Lesson 3: Developing Formulas for volume for multiple shapes
      • Lesson 4: Application of Area vs. Volume
    • Module 2
      • Lesson 1: Classifying Triangles
      • Lesson 2: Introduction to Trigonometry
      • Lesson 3: Extending Trigonometry
      • Lesson 4: Properties and Characteristics of Triangles
    • Module 3
      • Lesson 1: Discovering Congruence
      • Lesson 2: Applying Congruence
      • Lesson 3: Developing Similarity
      • Lesson 4: Applying Similarity
  • FNGR
    • Module 1
      • Lesson 1: Identifying Exponential Functions
      • Lesson 2: Identifying Exponential Growth and Decay
      • Lesson 3: Transformations of Parent Functions, focus on Exponential
      • Lesson 4: Transformations, Vertical and Horizontal, of Parent functions
    • Module 2
      • Lesson 1 | Identify Functional Relationships
      • Lesson 2: Identify Horizontal and Vertical Shifts of Quadratics
      • Lesson 3: Build Functions
      • Lesson 4: Recognize Algebraic Representation of Quadratics and Transformations

POLQ 3 | Lesson 3 | Solutions (Understanding Multiplicity)

Solutions:

 

1: a

2: c

3: b

4: d

 

Return to Explore (Understanding Multiplicity)

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  • LINR
    • Module 1
      • Lesson 1: Linear Patterns and Multiple Representations
      • Lesson 2: Graphs and Equations of Linear Situations
      • Lesson 3: Graphs in Slope-Intercept Form
      • Lesson 4: Writing the Equation of a Line
    • Module 2
      • Lesson 1: Solving Equations Including Absolute Value
      • Lesson 2: Solving Equations and Inequalities (Including Absolute Value)
      • Lesson 3: Linear Inequalities in Two Variables
    • Module 3
      • Lesson 1: Analyzing, writing, and solving linear systems
      • Lesson 2: Writing, solving, interpreting linear systems of inequalities
      • Lesson 3: Understanding and Using Absolute Value
      • Lesson 4: Solving Linear Systems with Geometric Applications
  • RATL
    • Module 1
      • Lesson 1: Operations on Fractions
      • Lesson 2: Using Percentages
      • Lesson 3: Multiplicative Thinking
      • Lesson 4: Proportional Reasoning
    • Module 2
      • Lesson 1: Introduction to Rational Expressions
      • Lesson 2: Adding and Subtracting Rational Expressions
      • Lesson 3: Multiplying and Dividing Rational Numbers
      • Lesson 4: Solving rational equations and writing rational equations from contextual situations
    • Module 3
      • Lesson 1: Evaluating Rational Expressions
      • Lesson 2: Solving Rational Inequalities
      • Lesson 3: Zeros and Asymptotes of Rational Functions
      • Lesson 4: Graphing Rational Functions
  • POLQ
    • Module 1
      • Lesson 1: Multiplication of Polynomials
      • Lesson 2: Division of Polynomials
      • Lesson 3: Factoring Polynomials
      • Lesson 4: Summative Polynomial Performance Task
    • Module 2
      • Lesson 1: Special Factoring Patterns
      • Lesson 2: Completing the square to solve quadratic equations
      • Lesson 3: Solving Radical Equations
      • Lesson 4: Deriving the quadratic formula
    • Module 3
      • Lesson 1: Introduction to Graphing Polynomials
      • Lesson 2: Roots of Polynomials and Polynomial Theorems
      • Lesson 3: Polynomials features: multiplicity, degree, end behavior
      • Lesson 4: Applications of Polynomials
  • GEOM
    • Module 1
      • Lesson 1: Developing formulas for area of multiple shapes
      • Lesson 2: Extending and Applying Area and Perimeter
      • Lesson 3: Developing Formulas for volume for multiple shapes
      • Lesson 4: Application of Area vs. Volume
    • Module 2
      • Lesson 1: Classifying Triangles
      • Lesson 2: Introduction to Trigonometry
      • Lesson 3: Extending Trigonometry
      • Lesson 4: Properties and Characteristics of Triangles
    • Module 3
      • Lesson 1: Discovering Congruence
      • Lesson 2: Applying Congruence
      • Lesson 3: Developing Similarity
      • Lesson 4: Applying Similarity
  • FNGR
    • Module 1
      • Lesson 1: Identifying Exponential Functions
      • Lesson 2: Identifying Exponential Growth and Decay
      • Lesson 3: Transformations of Parent Functions, focus on Exponential
      • Lesson 4: Transformations, Vertical and Horizontal, of Parent functions
    • Module 2
      • Lesson 1 | Identify Functional Relationships
      • Lesson 2: Identify Horizontal and Vertical Shifts of Quadratics
      • Lesson 3: Build Functions
      • Lesson 4: Recognize Algebraic Representation of Quadratics and Transformations
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