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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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