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Algebra I Recipe: Factoring Special Products
A. Factoring using the GCF
  1. Find the largest number common to every coefficient or number.


  2. Find the GCF of each variable.
    • It will always be the variable raised to the smallest exponent.

  3. Find the terms that the GCF would be multiplied by to equal the original polynomial.
ExamplesExamples:
3x2 - 6x

2x2 - 4x + 8

5x2y3 + 10x3y

B. Factoring the Difference of Two Squares
  1. The factors will always be (a + b)(a – b).
  2. "a" is the square root of the first term
  3. "b" is the square root of the second term.
ExamplesExamples:
9x2 - 49

121x2 - 100

25x2 - 64y2

C. Factoring a Perfect Square Trinomial
  1. Characteristics
    • "ax2" term is a perfect square.
    • "c" term is a perfect square.
    • "c" term is positive.
    • Factors into two identical binomials: (a ± b)2.

  2. Steps to Factor
ExamplesExamples:
9x2 - 30x + 25

4x2 + 28xy + 49y2

2x2 + 16x + 32

16x3 + 80x2 + 100x




G Redden

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