Lesson 3: Polynomial Equations of Higher Degree

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Lesson 3 Polynomial Equations of Higher Degree

• Section P1, 2.3, 2.4
• Carrie, Lauren, Meghan, Hayley

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Objectives

• Definition of a higher degree polynomial
• Solving a higher degree polynomial by factoring
• Solve a higher order degree polynomial using the
  remainder theorem, factor theorem, and synthetic
  division GIVEN 1 solution or using a graphing
  calculator to find 1 rational root
• Solve a higher order degree polynomial involving
  complex solutions

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Definition of a Higher Degree Polynomial

• Any equation that is not linear or quadratic
• The equation is

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Solving a Higher Degree Polynomial by Factoring

• The problem
• Step 1- Set the equation equal to zero
• Step 2- factor
• Step 3- factor completely

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• Step 4- set each factor to zero
• You can check these solutions by substituting in
  the original equation.

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• Problem 2
• Step 1- group terms
• Step 2- Factor by grouping
• Step 3- Distributing property

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• Step 4- Set your factors equal to zero
• The solutions are 3,

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Solve a Higher Order Degree Polynomial
Using the Remainder Theorem, Factor Theorem, and
Synthetic Division GIVEN 1 solution
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• The Problem
• Step 1 graph the problem to find a function
• (either 2, -1, or -3)
• Step 2 Use synthetic division with the factor
  (x3)

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• Step 3 Factor the quadratic equation
• Step 4 complete the factorization
• Note that this factorization implies that f has
  four real zeros.

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Solve a Higher Order Degree Polynomial Involving
Complex Solutions

• The problem
• Step 1 Graph the problem to find its functions
  (either -2 or 3)
• Step 2 Use synthetic division with the factor
  (x-3)

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• Step 3 Use synthetic division again using the
  factor (x2)
• Step 4 Put the problem in standard form
• Step 5 Put the problem into the quadratic
  formula

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Learning Opportunity!!! WOO-HOO!!!

• Factoring Page 12 141,143,149
• Synthetic Division Page 164 51,59 Page 181 7
• Complex Solutions Page 182 61-65 odd