• When factoring trinomials where a ≠ 1, two main methods are used: Guess and Check and Factoring by Grouping.
  • Guess and Check.
    • When using this method, you simply try every solution you can until it factors out.
      • Ex. 2x2+9x-5
      • Find the Factors of -5 = 1,-5 and -1,5
      • Guess and Check
        • (2x-1)(x+5) or (2x+1)(x-5)
        • the first one solves to be 2x2+ 9x-5 (the right answer) and the second one solves to be 2x2-9x-5 (the wrong answer)
  • Factoring by Grouping.
    • When using this method, you separate the two factorial statements by undergoing a series of steps
      • Factor: ax2+bx+c
      1. First, multiply a and c=ac
      2. Second, find two factors of ac whose sum is b.
      3. Third, split the middle term by using the two factors.
      4. Then, group the first two and last two terms.
      5. Last, factor out the GCF from each group and rewrite.
         • Example: 6x2-13x-5
           1. 6*-5=-30
           2. -15+2=-13 and -15*2=-30
           3. 6x2-15x+2x-5
           4. (6x2-15x)+(2x-5)
           5. 3x(2x-5)+(2x-5)
           6. (3x+1)(2x-5)

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