College Algebra / Unit 2 Alg 086 worked example, 60 to 90 seconds
Factoring ax² + bx + c by Grouping
The idea
Factoring by grouping splits the middle term into two terms whose coefficients multiply to ac and add to b, then factors each half.
In practice
Factor 2x² + 7x + 3. Here ac = 2 · 3 = 6 and b = 7; the pair 6 and 1 multiplies to 6 and adds to 7. Split the middle: 2x² + 6x + x + 3. Group and factor each half: 2x(x + 3) + 1(x + 3). The shared binomial factors out: (x + 3)(2x + 1). FOIL back: 2x² + x + 6x + 3 = 2x² + 7x + 3 — the original returns. The pair hunt is the whole search; the rest is the GCF move run twice.
Where people slip
If no integer pair multiplies to ac and adds to b, the trinomial does not factor over the integers.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
Builds on
- Nothing. This is a starting point.
Unlocks
- Nothing yet depends on this.
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