Unit 59: Advanced Algebra (Polynomials, Factoring)

Day 10 of 30

Factoring: GCF

11-12Mathematics

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Learning Objective

Students will explore factoring and gcf through guided practice and application.

Today's Lesson

This lesson focuses on factoring: gcf. 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 factoring: gcf. 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

Factor: x² + 7x + 12

Hint: Find two numbers that multiply to 12 and add to 7.
2

Factor: x² - 9

Hint: Difference of squares.
3

Factor completely: 2x² + 8x

Hint: GCF first.

Teaching Tip

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

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