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4.4B Factoring Quadratics: Leading Coefficient ≠ 1 : Pattern (ac)

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

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4.4B Factoring Quadratics: Leading Coefficient ≠ 1 : Pattern (ac)

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  1. 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”

  2. 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

  3. More examples: • 2. 6x² + x – 2 a=6 b=1 c= -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

  4. 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

  5. Think Alouds • 1. 3x² + 10x – 8 • 2. 4x²+ 5x – 6 • 3. 80x² + 68x +12 • 4. 42x² + 35x + 7

  6. 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

  7. Examples: Difference of 2 squares: LC ≠1 • 1. 16x² - 1 • 2. 36x² - 9 • 3. 9x² - 64

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