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Factoring Strategies in Beginning Algebra

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  • What is the first step in factoring an expression?
    Check if there is a Greatest Common Factor (GCF) for all terms and factor it out first.
  • How do you decide the factoring method based on the number of terms?
    2 terms: Check for difference of squares, cubes, or sum of cubes.
    3 terms: Check if quadratic and factor by grouping or as a perfect square trinomial.
    4 terms: Try factoring by grouping.
  • What should you check about the first and last terms when factoring?
    Check if the first and last terms are perfect squares. If yes, see if it forms a perfect square trinomial.
  • What are the special factoring cases to recognize?
    Difference of squares: \(a^2 - b^2\)
    Sum or difference of cubes: \(a^3 \pm b^3\)
  • When can you use factoring by grouping?
    Usually for 4 terms, but sometimes for 3 terms if you split the middle term.
  • What should you do after each factoring step?
    Always check if the expression is already factored as much as possible and factor further if you can.