Introduction to Polynomial Basics

Page 1: Introduction to Polynomial Basics

• Objective: Create and evaluate expressions involving polynomials.

• Scenario: Earl is constructing a doghouse which has:

  • Front Shape: A square and a triangle on top of it.

  • Rectangular Door: Allows the dog to enter.

• Earl needs to determine the area of the front of the doghouse to buy the right amount of paint.

• Measurements (refer to Figure 1) will guide the creation of a mathematical expression involving various variable terms.

Page 2: Area of the Square

• Formula for Area of Square: A = s²

• Calculating Area:

  • s = 2x

  • A = (2x)² = 4x²

Page 3: Area of the Triangle

• Formula for Area of Triangle: A = 1/2 * b * h

• Calculating Area:

  • b = 2x

  • h = 3/2

  • A = 1/2 * (2x) * (3/2) = 3/2 x

Page 4: Area of the Rectangular Door

• Formula for Area of Rectangle: A = l * w

• Calculating Area:

  • l = x

  • w = 1

  • A = x * 1 = x

• Total Area Calculation:

  • Combine areas: Area = Area of Square + Area of Triangle - Area of Door.

  • Total Area = 4x² + 3/2 x - x

Page 5: Module Summary

• Focus: The module will examine expressions that combine several variable terms, emphasizing polynomial expressions in practical scenarios.

• Author and Licensing Information:

  • Content reference: Lumen Learning, OpenStax. Licensed under CC BY, indicating that attribution is required for reuse.