4.4B Factoring Quadratics: Leading Coefficient ≠ 1 : Pattern (ac) Divide out a common monomial if possible. Multiply (a)(c) Use the “X” to find factors.

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4.4B Factoring Quadratics: Leading Coefficient ≠ 1 : Pattern (ac) Divide out a common monomial if possible. Multiply (a)(c) Use the “X” to find factors of (ac) and b Use Lead coefficient with x FIRST in each factor Use factors of (ac) and b SECOND in each factor Divide if possible from each factor to get final factors. Check by “FOIL”

Examples 1. 2x² + 5x + 2 a = 2 b= 5 c=2 ac = (2)(2) = 4 find multiples of 4 that ADD up to 5 “X” 4 and 1 are the factors Lead coefficient is 2: use 2 in both ( ) with x (2x + 4)(2x + 1)Divide first ( ) by 2 (x + 2)(2x + 1)FACTORS!!! Check by FOIL : 2x² + 1x + 4x + 2 = 2x² + 5x + 2

More examples: 2.6x² + x – 2 a=6b=1c= -2 ac = (6)(-2) = -12 Multiples of -12 that have sum of b or 1 (“X”) Multiples are 4 and -3 Lead coefficient = 6, so use 6x in both ( ) (6x + 4)(6x – 3)divide first by 2 and second by 3 (3x + 2)(2x – 1) FACTORS Check by “FOIL”6x² -3x +4x – 2 = 6x² +x -2

More examples 3. 8x² - 20x – 12 divide out 4 4(2x² -5x -3) a=2 b= -5 c= -3 ac = (2)(-3) = -6 multiples of -6 that add up to -5 “X” multiples are -6 and 1 Lead coefficient of ( ) is 2: use 2x in each ( ) (2x – 6)(2x +1) Divide first by 2 4(x – 3) (2x + 1) FACTORS!! check by “FOIL” 4(2x²+x-6x-3)=4(2x²-5x-3)=8x²-20x-12

Think Alouds 1. 3x² + 10x – x²+ 5x – x² + 68x x² + 35x + 7

4.4A Factoring: Leading Coefficient ≠1 Factoring Difference of 2 Squares LC ≠ 1 2 terms SUBTRACTION Both have NICE Square roots Put square roots of each in the ( ) ( + )( - ) : Use one of each sign

Examples: Difference of 2 squares: LC ≠1 1.16x² x² x² - 64