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R EVIEW & 6.6 T HE F UNDAMENTAL T HEOREM OF A LGEBRA Reviewing: Equivalent statements Multiplicities Rational Root Theorem Irrational Root Theorem Introducing:

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Presentation on theme: "R EVIEW & 6.6 T HE F UNDAMENTAL T HEOREM OF A LGEBRA Reviewing: Equivalent statements Multiplicities Rational Root Theorem Irrational Root Theorem Introducing:"— Presentation transcript:

1 R EVIEW & 6.6 T HE F UNDAMENTAL T HEOREM OF A LGEBRA 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 List all different factoring methods as a review of 6.4/6.5/6.6 for Monday’s Quiz

2 Z EROS, X -I NTERCEPTS, S OLUTIONS (R OOTS ), AND F ACTORS OF P OLYNOMIALS

3 M ULTIPLICITY ( THE EXPONENT OF THE F ACTOR ): F OR E VEN M ULTIPLICITY THE G RAPH ONLY T OUCHES A T THE X-I NTERCEPT F OR O DD M ULTIPLICITY THE G RAPH C ROSSES AT THE X-I NTERCEPT

4 R ATIONAL R OOT T HEOREM : C ONSTANT T ERM AND THE L EADING C OEFFICIENT P(x) = 2 x 3 – 6 x x - 8

5 P(x) = x 2 – 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) = x 2 – 2x + 2

6 P(x) = x 4 + x 3 + 2x 2 + 4x – 8 How many factors should this polynomial expression have?


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