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Factoring Special Patterns

General Rules for Factoring

Use this checklist to help determine how to factor a polynomial:
  • Factor out the greatest common factor first, if possible.
  • If the polynomial to be factored is a binomial, then it may be a difference of two squares, or a sum or difference of two cubes (remember that a sum of two squares does not factor).
  • If the polynomial to be factored is a trinomial, then:
    • the polynomial may be a perfect square if two of the three terms are perfect squares.
    • the polynomial may be one of the general forms.
  • If the polynomial to be factored consists of four or more terms, try factoring by grouping.
  • Check if any of the factors can be factored further and do so when necessary.
  • Finally, check the factoring by multiplying the factors to determine if they equal the original polynomial.