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Factoring Quadratics mini-quiz

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1 We need to factor 4x2 – 15x + 9.
First, find the value of "a times c":
 
  ac = 4
  ac = 9
  ac = –15
  ac = 36
  ac = 13
2 The factors of ac need to add up to:
 
  15
  –15
  13
  –13
  None of the above
  3 For the factors of ac, we need:
 
  both factors to be negative.
  both factors to be positive.
  one factor to be positive and
the other factor to be negative.
4 The factor pair that works is:
 
  1 and 15
  –1 and 15
  –6 and –6
  –3 and –12
  None of the above.
5 Then the "box" set-up looks like:
 
  first row: 4x^2 and 1; second row: 15 and 9 
  first row: 4x^2 and -6x; second row: -6x and +9 
  first row: 4x^2 and -3; second row: -12 and +9 
  first row: 4x^2 and -1x; second row: +15x and +9 
  first row: 4x^2 and -3x; second row: -12x and +9 
6 Then 4x2 – 15x + 9 factors as:
 
  (2x + 3)(2x + 3)
  (4x + 1)(4x + 15)
  (4x – 3)(x – 3)
  (2x – 3)(2x – 3)
  (4x + 9)(x + 1)


 

 

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