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Summarizing the General Strategy for Factoring Polynomials

Key Concepts

  • General Strategy for Factoring Polynomials See the figure below.
    This figure presents a general strategy for factoring polynomials. First, at the top, there is GCF, which is where factoring starts. Below this, there are three options, binomial, trinomial, and more than three terms. For binomial, there are the difference of two squares, the sum of squares, the sum of cubes, and the difference of cubes. For trinomials, there are two forms, x squared plus bx plus c and ax squared 2 plus b x plus c. There are also the sum and difference of two squares formulas as well as the “a c” method. Finally, for more than three terms, the method is grouping.
  • How to Factor Polynomials
    1. Is there a greatest common factor? Factor it out.
    2. Is the polynomial a binomial, trinomial, or are there more than three terms?
      • If it is a binomial:
        Is it a sum?
        • Of squares? Sums of squares do not factor.
        • Of cubes? Use the sum of cubes pattern.
        Is it a difference?
        • Of squares? Factor as the product of conjugates.
        • Of cubes? Use the difference of cubes pattern.
      • If it is a trinomial:
        Is it of the form \({x}^{2}+bx+c\)? Undo FOIL.
        Is it of the form \(a{x}^{2}+bx+c\)?
        • If ‘a’ and ‘c’ are squares, check if it fits the trinomial square pattern.
        • Use the trial and error or ‘ac’ method.
      • If it has more than three terms:
        Use the grouping method.
    3. Check. Is it factored completely? Do the factors multiply back to the original polynomial?

This lesson is part of:

Factoring and Factorisation I

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