Solving polynomial inequalities

Lessons

• Introduction
  What is an Inequality?

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• 1.
  Solving Linear Inequalities
  Solve:
  a)

  $3x-10$ > $11$
  
  
  b)

  $5-2x \leq 13$
  
  

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• 2.
  Solving Quadratic Inequalities
  Solve each inequality
  i)

  graphically
  ii)

  algebraically using test intervals.
  a)

  $2x^2-x-15 \geq 0$
  
  
  b)

  $-5x^2-10x+40$ > $0$
  
  

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• 3.
  Solving Higher Degree Polynomial Inequalities:
  Solve:
  a)

  $23(x+5)(x-4)^3(x-3)^8(x+2)^{11} \geq 0$
  
  
  b)

  $23(x+5)(x-4)^3(x-3)^8(x+2)^{11}$ < $0$
  
  

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• 4.
  Factor First, then Solve Inequalities
  Solve: $-2x^4+3x^3+18x^2-17x-30 \leq0$

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