Summary of Factoring Techniques

• For all polynomials, first factor out the greatest common factor (GCF).

• For a binomial, check to see if it is any of the following:

  1. difference of squares: x² − y² = ( x + y) ( x − y)

  2. difference of cubes: x³ − y³ = ( x − y) ( x² + xy + y²)

  3. sum of cubes: x³ + y³ = ( x + y) ( x² − xy + y²)

• For a trinomial, check to see if it is either of the following forms:

  1. x² + bx + c:

     If so, find two integers whose product is c and whose sum is b. For example,
     

     
     

  2. ax² + bx + c:

     If so, find two binomials so that

     the product of first terms = ax²

     the product of last terms = c

     the sum of outer and inner products = bx

     See the following where the product of first terms = (3 x)(2 x) = 6 x², the product of last terms = (2)(−5) = −10, and the sum of outer and inner products = (3 x)(−5) + 2(2 x) = −11 x.
     

     
     

  3. 
     

     
     

• For polynomials with four or more terms, regroup, factor each group, and then find a pattern as in Steps 1 through 3.

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