Factoring Binomials

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Factoring Binomials

• 5.6
• SSC 105

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Factoring Binomials

• Difference of Squares a2 b2 (a b)(a
  b)
• Difference of Cubes a3 b3 (a b)(a2 ab
  b2)
• Sum of Cubes a3 b3 (a b)(a2 ab b2)

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Exercise 16

• Factor completely
• 25x2 144
• A) (5x 12)2
• B) (5x 12)2
• C) (5x 12)(5x 12)
• D) (25x 12)(5x 12)

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Another example
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Exercise 17

• Factor completely
• 8x3 27  
• A) (2x 3)3
• B) (2x 3)(4x2 6x 9)
• C) (2x 3)(4x2 6x 9) 
• D) The polynomial is prime.

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More examples
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Exercise 18

• Factor completely
• 8t3 5  
• A) (2t 2)3
• B) (2t 3)(4t2 6t 9)
• C) (2t 3)(4t2 6t 9) 
• D) The polynomial is prime.

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A Factoring Strategy

• Factor out the greatest common factor (Section
  5.4).
• Identify whether the polynomial has two terms,
  three terms, or more than three terms.
• If the polynomial has more than three terms,
  try factoring by grouping (Section 5.4 and
  Section 5.6).
• If the polynomial has three terms, check first
  for a perfect square trinomial. Otherwise, factor
  the trinomial with the grouping method or the
  trial-and-error method (Section 5.5).
• If the polynomial has two terms, determine if
  it fits the pattern for a difference of squares,
  difference of cubes, or sum of cubes. Remember, a
  sum of squares is not factorable over the real
  numbers (Section 5.6).