Unit 60: Quadratic Functions and Equations

Day 11 of 30

Solving by factoring

11-12Mathematics

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Learning Objective

Students will solve by factoring through guided practice and application.

Today's Lesson

This lesson focuses on solving by factoring. Mathematics provides tools for modeling and analyzing complex systems.

Factoring is writing an expression as a product of simpler expressions. It's the reverse of distributing. For example, 6x + 9 factors to 3(2x + 3) because 3 is common to both terms. Factoring: 1) Find the greatest common factor (GCF). 2) Divide each term by the GCF. 3) Write GCF times what remains. Factoring simplifies expressions and is essential for solving equations. It reveals structure and makes complex problems simpler!

As you engage with this material, consider both the theoretical foundations and practical applications. Think critically about how this concept builds on prior knowledge and where you might apply it beyond the classroom.

Challenge yourself to go beyond memorization—seek to understand the "why" behind the processes and principles.

Key Terms
Problem

A mathematical question requiring analysis and solution

Solution

The result obtained by solving a problem

Activities
Instructions
1. Review the example problems for solving by factoring. 2. Identify the steps and strategies used. 3. Work through practice problems independently. 4. Compare solutions with a partner.
Materials Needed
  • Notebook
  • Calculator (if needed)
  • Graph paper
Practice Problems
1

Solve for x: x + 7 = 15

Hint: Subtract 7 from both sides.
2

Solve for y: 3y = 12

Hint: Divide both sides by 3.
3

If 2x - 5 = 9, what is x?

Hint: Add 5 to both sides, then divide by 2.

Teaching Tip

For advanced learners: Encourage deeper analysis and real-world connections. Consider extension activities that allow students to apply solving by factoring to novel situations.

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