Warm Up Factor out the GCF 1.-5x x x 3 +4x Factor 3. 4.

Warm Up Answers

Lesson 12.5 Factoring Special Cases

Use 7 Steps: step 1: write it in standard form step 2: factor out GCF if possible step 3: Write what a, b, and c = step 4: write 2 sets of ( ) put ax in each set step 5: multiply a and c step 6: what factors of step 5 add up to b? step 7: simplify each set of ( ) if you can

Special Cases: Factoring a Difference of Squares Factoring a difference of squares follows the same process as before. Just remember that the middle term is 0x. (x )(x ) Think what are the factors of ac which will give 0.

You Try

Do you notice a pattern with the difference of two squares? They follow this rule: A 2 – B 2 = (A-B)(A+B) Square root both A and B terms and then put B as a negative and postive. X 2 – 81 The square root of x 2 = x and the square root of 81 is 9. Therefore it factors to (x+9)(x-9).

Special Cases: Perfect Square Trinomials Factoring perfect square trinomials follows the same seven step process as before. (2x )(2x ) (2x – 6)(2x-6)

You Try

Do you notice a pattern with perfect square trinomials? Follow these rules: A 2 + 2AB + B 2 = (A+B) 2 A 2 – 2AB + B 2 = (A–B) 2

Try these with new rules!! 1)64x 2 – 16x + 1 2)4x 2 + 4x + 1

Summary What is a perfect square trinomial and how is it factored?