Intermediate Algebra — 3.1: Factoring Trinomials When a ≠ 1 скачать в хорошем качестве

Intermediate Algebra — 3.1: Factoring Trinomials When a ≠ 1

The simple trick of dropping diamond numbers straight into binomials breaks when the leading coefficient isn't 1. This lesson teaches the diamond method combined with factor by grouping — a reliable six-step process that handles every trinomial, including tricky negative cases. Key concepts covered: • Why the standard diamond shortcut fails when a ≠ 1 (the leading term becomes ax², not x²) • The four-step pre-factoring checklist: standard order, positive lead, GCF, and term count • Setting up the diamond: b on top, a · c on bottom, and finding two numbers that add to b and multiply to a · c • Sign-logic guide for choosing diamond numbers when negatives are involved • Splitting the middle term and factoring by grouping step by step • The critical debugging rule: if parentheses don't match after grouping, factor out the opposite sign • Full worked examples: 3x² + 11x + 6 and 8x² − 22x + 5 • FOIL verification to confirm every answer • Practice problem: 6x² + 19x + 10 (pause and try it yourself) ━━━━━━━━━━━━━━━━━━━━━━━━ SOURCE MATERIALS The source materials for this video are from    • Intermediate Algebra Lecture 6.4:  Factori...