Algebra II/Factoring Rules

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1. GCF[edit | edit source]

Always take out the greatest common factor first!

  • 6x2y3 - 10xy5 = 2xy3(3x - 5y2)
  • (x+y)a4b9c + (x+y)a2bc5 = (x+y)a2bc(a2b8 + c4)

2. Difference of two squares: a2 - b2 = (a+b)(a-b)[edit | edit source]

  • 9x2 - 49y2 = (3x-7y)(3x-7y)
  • 121x2 - 64 = (11x - 8)(11x + 8)
  • 3x2 - 12 = 3(x2 - 4) → 3(x+2)(x-2)
  • 3h2 - 48 = 3(h2 - 16) → 3(h-4)(h+4)

3. Trinomial whose leading coefficient is one[edit | edit source]

Attention
The second is the sum, the third is the product
  • 3x2 - 18x + 24 = 3(x2 - 6x + 8) → 3(x-4)(x-2)
  • a2b2 + 4ab - 96 = (ab-8)(ab+12)

4. Sum of two cubes: a3 + b3 = (a+b)(a2 - ab + b2)[edit | edit source]

Attention
SOAP: Same, Opposite, AlwaysPositive
  • x3 + 125 = (x+5)(x2 - 5x + 25)
  • 27x3 + 8 = (3x+2)(9x2 - 6x + 4)
  • 1000c3 - 343b3 = (10c - 7b)(100c2 - 70bc + 49b2)
  • 8x3 - 729 = (2x - 9)(4x2 - 18x + 81)

5. Perfect Square Trinomials: a2 + 2ab + b2 = (a+b)2[edit | edit source]

  • 9x2 + 30x + 25 = (3x + 5)(3x + 5)
  • 36c2 + 132cd + 121d2 = (6c+11d)(6c+11d)

6. Factor by Grouping[edit | edit source]

  • b3 - 3b2 + 4b - 12 = (b-3)(b2 + 4)
  • cm3 - dm3 - 8c + 8d = m3(c-d) - 8(c-d) → (m-2)(m2 + 2m + 4)(c–d)