Review & 6.6 The Fundamental Theorem of Algebra

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Presentation transcript:

Review & 6.6 The Fundamental Theorem of Algebra Reviewing: Equivalent statements Multiplicities Rational Root Theorem Irrational Root Theorem Introducing: Fundamental Theorem of Algebra and it’s corollary (very intuitive) Complex Conjugate Root Theorem Demonstrating: Factoring polynomials with the help of a graphing calculator Analyzing answer and graph afterwards Performing: 6.5 Practice B questions 5 - 9, 6.6 Practice B questions 5 - 9 List all different factoring methods as a review of 6.4/6.5/6.6 for Monday’s Quiz

Zeros, x-Intercepts, Solutions (Roots), and Factors of Polynomials

Multiplicity(the exponent of the Factor): For Even Multiplicity the Graph only Touches At the X-Intercept For Odd Multiplicity the Graph Crosses at the X-Intercept

Rational Root Theorem: Constant Term and the Leading Coefficient P(x) = 2x3 – 6x2 + 12x - 8

Complex Conjugate Root Theorem P(x) = x2 – 3 If a+bi is a root of a polynomial equation with real-number coefficients, then a-bi is also a root Complex Conjugate Root Theorem P(x) = x2 – 2x + 2

How many factors should this polynomial expression have? P(x) = x4 + x3 + 2x2 + 4x – 8