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.
Examples:
 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.
Examples:
 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
Examples:
 9x2 - 30x + 25
 4x2 + 28xy + 49y2
 2x2 + 16x + 32
 16x3 + 80x2 + 100x

G Redden

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