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Factoring Strategies and Formulas

When asked to factor , always factor out any Greatest Common Factor [GCF]
before using any other method. Then your choice of technique depends on the
number of terms .

1. Two Terms
  • If the terms are perfect squares, use Difference of Squares
Formula first .
  • If possible, use Difference of Cubes or Sum of Cubes
Formula.

2. Three Terms
  • Use the Trial and Error Method
  • Or Use the alternate method called either “AC, By Grouping”,
“FOIL”, or “Master Product”.
Note: the Riverside Learning Lab has a handout called Factoring Trinomials ,
which displays both these methods.

3. Four Terms—
  • Use the “ By Grouping ” method.

When finished make sure the GCF is listed as a factor and no GCF remains in
any of the factors. Also look at the binomial factors for a remaining Difference
of Squares , Difference of Cubes, or Sum of Cubes.

Special Product Formulas

I. Difference of Squares ~ Conjugates

II. Perfect Square

III. Sum of Cubes

IV. Difference of Cubes

For clarity you may wish to use the a & b version if the problem contains x or
y. Alternately, use the x and y, if the problem contains a or b.

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