2. (reverse of Distributive Property; factor out the common stuff) 6x – 9 = 2·3·x - 3·3 = 3(2x – 3) 5x 2 + 8x = 5·x·x + 2·2·2·x = x(5x+8) 10x 3 –15x 2 =2·5·x·x·x-3·5·x·x=5x 2 (2x-3) x 2 + 3x – 4 = x·x + 3·x - 2·2 = x 2 + 3x – 4 (nothing common)

3.  Group first two terms; make sure third term is addition; group last two terms  Common Monomial Factor both parentheses (inside stuff must be same in both parentheses)  Answer: (Outside stuff)·(Inside stuff)  5x 2 – 3x – 10x + 6 = (5x 2 – 3x) + ( – 10x + 6) = x(5x-3) – 2(5x – 3) = (x – 2)(5x – 3)

4.  Find two numbers r & s, so that r + s = b and r ·s = a · c a=2 b=7 c= - 15 r+s = 7 r·s = 2(-15) = -30 -1· - 30= - 301+ - 30= - 29 2 · - 15= - 302+ - 15= - 13 3 · - 10= - 303+ - 10= - 7 5· - 6= - 245+ - 6= - 1 2x 2 + 7x – 15 2x 2 - 3x + 10x – 15 (2x 2 - 3x) + (10x – 15) x(2x - 3) + 5(2x – 3) (x + 5)(2x – 3)

5.  List factor pairs of a; these are the possible coefficients of x in the two parentheses.  List factor pairs of c; these are the possible constant terms in the two parentheses.  Guess by combining the factor pairs of both a & c then compare the sum of the Outer and Inner multiplications to b.  If the check works you have your answer; if not guess again. a=2 b=7 c= - 15 Factor pairs of acac 121 -15 3 -5 5 -3 15 -1 2x 2 + 7x – 15 Guess #1: (x -1)(2x + 15) = 2x 2 + 15x – 2x – 15 = 2x 2 + 13x – 15 error Guess #2:(x + 5)(2x – 3) = 2x 2 -3x + 10x – 15 = 2x 2 + 7x – 15 correct Therefore (x + 5)(2x – 3) is your answer.

6.  Find two numbers, r & s, so that r + s = b and r · s = c  Answer: (x + r)(x + s) a=1 b=5 c= - 24 r+s = 5 r·s = - 24 1· - 24= - 24 1+ - 24= - 23 2 · - 12= - 242+ - 12= - 10 3 · - 8= - 243+ - 8= - 5 4 · - 6= - 244+ - 6= - 2 6 · - 4= - 246+ - 4=2 8 · - 3= - 248+ - 3=5 12 · - 2= - 2412+ - 2=10 24· - 1= - 2424+ - 1=23 x 2 + 5x – 24 = (x+8)(x-3)

7.  Find square roots of both terms  Answer: (a + b)(a – b) 25x 2 - 49 =(5x) 2 – (7) 2 =(5x + 7)(5x – 7) x2x2 x 11 42 93 164 255 366 497 648 819 10010 12111 14412

8.  Find square roots of first & last terms  Use sign of the middle term  Answer: (a ± b) 2 16x 2 - 40x + 25 =(4x – 5) 2 √ 2(4x)(-5) = -40x x2x2 x 11 42 93 164 255 366 497 648 819 10010 12111 14412

9. Flowchart Common Monomial Difference of Two Squares Factor by Grouping r & s method with shortcut Number of terms 2 3 4 Does a = 1? yes no r & s method without shortcut Do you know square root of first and last terms? yes no Perfect Square Trinomial Does 2ab part work? yes no