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1.5 Polynomial Functions 2 and Complex Zeros

Part of Polynomial and Rational Functions in AP® Precalculus. Read the opening section, then create a free account for the full interactive lesson, practice, and progress tracking.

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In Topic 1.5 of AP Precalculus, you connect the algebraic roots of a polynomial to its factors and graphical behavior.

By the Fundamental Theorem of Algebra, any polynomial p(x) of degree n≥1 has exactly n complex zeros (counting multiplicities).\text{By the Fundamental Theorem of Algebra, any polynomial } p(x) \text{ of degree } n \geq 1 \text{ has exactly } n \text{ complex zeros (counting multiplicities).}
If a is a complex zero such that p(a)=0, then (x−a) is a linear factor of p(x).\text{If } a \text{ is a complex zero such that } p(a) = 0,\text{ then } (x - a) \text{ is a linear factor of } p(x).

In this unit

14 lessons

  1. 1.1Change in TandemPreview lesson
  2. 1.2Rates of ChangePreview lesson
  3. 1.3Rates of Change in Linear and Quadratic FunctionsPreview lesson
  4. 1.4Polynomial Functions and Rates of ChangePreview lesson
  5. 1.5Polynomial Functions 2 and Complex ZerosThis lesson
  6. 1.6Polynomial Functions and End BehaviorOpen lesson
  7. 1.7Rational Functions and End BehaviorOpen lesson
  8. 1.8Rational Functions and ZerosOpen lesson
  9. 1.9Rational Functions and Vertical AsymptotesOpen lesson
  10. 1.10Rational Functions and HolesOpen lesson
  11. 1.11Equivalent Representations of Polynomial and Rational ExpressionsOpen lesson
  12. 1.12Transformations of FunctionsOpen lesson
  13. 1.13Function Model Selection and Assumption ArticulationOpen lesson
  14. 1.14Function Model Construction and ApplicationOpen lesson

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