College Algebra / Unit 2 Alg 095 worked example, 60 to 90 seconds
Choosing a Factoring Strategy
The idea
Choosing a factoring strategy means running a fixed sequence: GCF first, then count terms and match the count to its methods, then check by multiplying back.
In practice
GCF comes out first, always. Two terms: test difference of squares, then sum or difference of cubes. Three terms: test perfect square trinomial, then the pair search for leading coefficient 1, then grouping. Four terms: factor by grouping. Run the sequence on 6x² + 21x + 9: the GCF 3 leaves 3(2x² + 7x + 3), and grouping finishes: 3(x + 3)(2x + 1). Multiply back: 3(2x² + 7x + 3) = 6x² + 21x + 9. Skipping the GCF would have hidden the small pair hunt inside bigger numbers.
Where people slip
Factor completely: a finished answer contains no factorable piece, and the multiply-back check runs on the whole product.
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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