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.
• It looks like the distributive property when in factored form ….. GCF(terms).

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.

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
• Write it as (a ± b)² since it factors into two identical binomials.
• "a" is the square root of the "ax²" term.
• "b" is the square root of the "c" terml.
• The operation in the binomial factor is the same as the operation in front of the "x" term.

Practice Problems