Factoring Examples & Practice

Calculus Readiness · Axiom Academy

EXAMPLE Factoring Worked Examples Every major factoring technique, one worked example at a time. Factoring is pattern recognition. Once you have seen each pattern enough times, you will spot which technique applies in a few seconds. These examples cover all the patterns you need — work down each one and watch the structure repeat. Rewrite each polynomial as a product of factors . The check is always the same: multiply the factors back out and confirm you land on the original expression. Every example below passes that check. An area model for the GCF. The two tiles 6x^2 and 9x share a common width 3x ; pulling it out leaves the height 2x + 3 , so 6x^2 + 9x = 3x(2x + 3) . Factoring is just reading a product off the shared dimension. Category 1 — Greatest Common Factor (GCF) Category 2 — Difference of Squares Hidden difference of squares — factor twice Category 3 — Simple Trinomial (leading coefficient 1 ) Category 4 — Harder Trinomial (AC method) Category 5 — Perfect Square Trinomial Category 6 — Factoring by Grouping Category 7 — Sum and Difference of Cubes Category 8 — Multi-Step Factoring Key Takeaways — the factoring workflow Run every factoring problem through the same checklist, in this order: GCF first. Always check for a common factor you can pull out before anything else. Count the terms. Two terms → difference of squares or sum/difference of cubes. Three terms → trinomial (simple, AC, or perfect square). Four terms → try grouping.

This is the written version of the interactive lesson above. See the full Calculus Readiness course.