(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)

 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)

 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= = · - 15= = · - 10= = - 7 5· - 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)

 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 x 2 + 7x – 15 Guess #1: (x -1)(2x + 15) = 2x x – 2x – 15 = 2x x – 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.

 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= = · - 12= = · - 8= = · - 6= = · - 4= =2 8 · - 3= =5 12 · - 2= =10 24· - 1= =23 x 2 + 5x – 24 = (x+8)(x-3)

 Find square roots of both terms  Answer: (a + b)(a – b) 25x =(5x) 2 – (7) 2 =(5x + 7)(5x – 7) x2x2 x

 Find square roots of first & last terms  Use sign of the middle term  Answer: (a ± b) 2 16x x + 25 =(4x – 5) 2 √ 2(4x)(-5) = -40x x2x2 x

Flowchart Common Monomial Difference of Two Squares Factor by Grouping r & s method with shortcut Number of terms 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