Chapter 10'8 Factoring Using the Distributive Property

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Chapter 10.8Factoring Using the Distributive
Property

• Algebra 1b
• Mrs. Cronquist

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Review Special Product Patterns

• Sum and Difference (or Difference of squares)
• (a b) (a b) a² b²
• Binomial Squared
• (a b)² a² 2ab b²
• (a b)² a² - 2ab b²

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Zero-Product Property

• If ab 0 then either a0 or b0
• Therefore if (x-4) (x3) 0
• Then x-40 or x30
• So x4 or x-3

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Factoring x² bx c

• Due to FOIL we know that
• (x p )(x q) if x (p q)x pq
• So now we are going to take quadratic functions
  and factor them.
• If the second sign is a sum then they have the
  same sign and that sign is the first sign If 2nd
  sum then same
• Now the sum of the factors of the 3rd must equal
  the 2nd.

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Factoring ax² bx c
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Special Products

• Difference of squares
• a² - b² (a b) (a b)
• 9x² - 16² (3x)² - 4² (3x 4)(3x 4)
• Perfect Square
• a² 2ab - b² (a b)²
• x² 8x 16 x² 2(4x) 4² (x 4)²
• a² - 2ab b² (a - b)²
• x² - 12x 36 x² - 2(6x) 6² (x - 6)²

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Find Common Factors

• The first step in factoring is to find the
  greatest common factor of each term.
• If we have ax² - bx we can factor out the x and
  we are left with x(ax b)
• If we have 2ax² 2bx we can factor out both the
  x and the 2 leaving 2x(ax b)

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Factor 14x? 21x²

• 14x? factors into 27xxxx
• 21x² factors into 37xx
• We can therefore factor out the 7x²
• This leaves 7x²(2x² - 3)

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Are these equations completely factored?

• 2x² 8 2(x² 8)
• 2x² - 8 2(x² - 4)

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Factor Completely

• 4x³ 20x² 24x
• 45x? 20x²

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Factor Completely

• -3w? 21w³
• 2d? 2d³ 60d²

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Factor by Grouping

• x³ 2x² 3x 6
• x³ - 2x² - 9x 18
• t³ t² 16t 16

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Solve by Factoring

• 8x³ 18x
• -30x? 58x³ 24x²
• 18x³ 30x² 60x

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Homework

• Worksheet
• s 3 29 odd
• OR
• Book pg 629
• s 15 48 m3