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5.6.08   Fundamental Theorem Of Algebra1
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5.6.08 Fundamental Theorem Of Algebra1

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  • 1. The Fundamental Theorem of Algebra If p ( x ) is any polynomial of degree n>1 with complex coefficients, then p ( x ) has at least one complex zero. A related theorem: A polynomial of degree n has at most n zeros.
  • 2. Finding Zeros:
  • 3. Multiplicity of Zeros: If a polynomial has the same zero more than once, we describe that zero’s multiplicity : Ex: Another theorem: A polynomial of degree n >1 with complex coefficients has exactly n complex zeros, if multiplicities are counted.
  • 4. Complex Zeros
  • 5.  
  • 6.  
  • 7.  
  • 8. Factoring Sums and Differences of Powers Recall that can be factored into . What about ?
  • 9. Find the cube roots of 8.