Special Case Factoring CCM2 11-7

Special Case Theorems Remember the Special Case Theorems Difference of Squares: (ax + b) (ax – b) = a2x2 – b2 Perfect Squares: (ax + b)2= a2x2 + 2abx + b2 We will use these theorems in reverse to help us factor As in all factoring, always check for a GCF before using these methods.

Difference in Squares Factoring Recognizing Quadratic Binomial Positive Leading Coefficient No Linear Term Negative Constant Theorem a2x2 – b2 = (ax + b) (ax – b) Example Factor 49x2 – 9 Square root the first term Square root the constant Combine the results with “+” and “-”

You Try: Factor the following: 25x2 - 4 81x2 - 49 4x2 - 36 (5x + 2)(5x – 2) (9x + 7)(9x - 7) 4(x + 3)(x - 3)

Perfect Squares Factoring Recognizing Quadratic Trinomial or the factors of ac are the same. Even if you do not recognize a perfect square, the other methods also work. Example Factor 4x2 +12x + 9 Note that So, , which is b Using the theorem: Perfect Squares Factoring Theorem

You Try: Factor the following: x2 + 6x + 9 4x2 - 4x + 1 9x2 + 24x + 16 (x + 3)2 (2x – 1)2 (3x + 4)2

Summary Thank You Factoring a Difference of Squares Factoring a Perfect Square Thank You