Factoring polynomials: $x^2 + bx + c$

Lessons

• Introduction
  a)

  "What is the cross-multiplying method of factoring? (a.k.a the Decomposition method)

  • - How does it work?
  • - How to use it?
  
  

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• 1.
  Factor the following
  
  a)

  ${x^2 +7x +10}$
  
  
  
  b)

  ${x^2-4x+4}$
  
  
  
  c)

  ${x^2+7x-30}$
  
  
  
  d)

  ${x^2-4x-21}$
  
  
  

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• 2.
  Factor with common factoring first
  
  a)

  ${4x^2+20x+24}$
  
  
  
  b)

  ${-4x^2 - 28x + 120}$
  
  
  
  c)

  ${x^2-12xy+36y^2}$
  
  
  
  d)

  ${-x^3y^2-3x^2y^3+4xy^4}$
  
  
  
  e)

  ${1\over4}{x^3-x^2-8x}$
  
  
  

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• 3.
  Factor with unusual exponents
  
  a)

  ${x^{6n}-3x^{3n}+2}$
  
  
  
  b)

  ${x^{2n}-7x^nx^m+10x^{2m}}$
  
  
  
  c)

  ${(x-2y)^2-8a(x-2y)+15a^2}$
  
  
  

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