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Grade 10 Math Lab: Proof & Generalization FREE

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Advanced Factoring

60 min Grade 10 Math Lab: Proof & Generalization

Learning Objectives

  • Factor complex trinomials
  • Factor by grouping
  • Recognize patterns

Key Concepts

AC Method

Multiply a×c, find factors that sum to b

Difference of Squares

a² - b² = (a+b)(a-b)

Theory

**AC Method for ax² + bx + c:** 1. Find ac product 2. Find factors of ac that sum to b 3. Rewrite middle term and factor by grouping **Example:** 2x² + 7x + 3 - ac = 6, factors: 1×6 (1+6=7 ✓) - 2x² + x + 6x + 3 - x(2x+1) + 3(2x+1) = (x+3)(2x+1)

Examples

Factor x² - 16

Solution: (x+4)(x-4) - difference of squares