Factoring

Factoring

Learn how to isolate variables step-by-step and solve any basic equation with confidence.

What You’ll Learn:

• 
  Greatest Common Factor (GCF)
• 
  Factor trinomials

• 
  Special products (difference of squares, etc.)
• 
  Avoid factoring mistakes

Lesson 1:

Greatest Common Factor (GCF)

Factor out the largest number or variable.

Example:
6x + 12
6(x + 2)
↑
GCF = 6

Lesson 2:

Trinomials (ax² + bx + c)

Find two numbers that multiply to ac and add to b.

Example: 

x² + 5x + 6 =
(x + 2)(x + 3)

Example:
x² + 5x + 6
(x + 2)(x + 3)
2 × 3 = 6
2 + 3 = 5

Lesson 3 :

Special Products

Difference of Squares

a² – b² = (a – b)(a + b)
Example:
x² – 9
(x + 3)(x – 3)

Perfect Square Trinomial

a² + 2ab + b² = (a + b)(a + b)

Example:
x² + 6x + 9
(x + 3)(x + 3)

Practice Problems Section

Easy

• Factor : 9x + 15

Medium

• Factor : x² + 7x + 10

Challenge

• Factor : 2x² + 7x + 3

Common Mistakes to Avoid

• 
  Forgetting the GCF
• 
  Wrong signs in binomials
• 
  Incorrect factor pairs

Quick Recap:
Factoring = Reverse of multiplying
(x + 2)(x + 3)
Factored
⟷
x² + 5x + 6
Expanded

Answer Key:
Easy:
3(3x + 5)
Medium:
(x + 5)(x + 2)
Challenge:
(2x + 1)(x + 3)

Next:

Quadratics



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