Fundamental Theorem of Algebra

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Notes 6.6 Fundamental Theorem of Algebra

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Presentation transcript:

Fundamental Theorem of Algebra PreCalculus 2-5

Fundamental Theorem

Fundamental Theorem

Fundamental Theorem

Fundamental Theorem

Fundamental Theorem

Fundamental Theorem

Find the complete factorization of the polynomial Fundamental Theorem

Fundamental Theorem

Fundamental Theorem

Examples of polynomials and their zeros Fundamental Theorem

Fundamental Theorem

Fundamental Theorem

Find the polynomial of degree 4 with zeros i, -i, 2 and -2 and with P(5)=273 Fundamental Theorem

Fundamental Theorem

Fundamental Theorem

Fundamental Theorem

Find the polynomial P(x) of degree 3 that has integer coefficients and zeros 1/3 and 5 – 2i Fundamental Theorem

Fundamental Theorem

Fundamental Theorem

Fundamental Theorem

Fundamental Theorem

Factor the polynomial completely into linear factors with complex coefficients Fundamental Theorem

Fundamental Theorem Consider the polynomial It is a fact that – 2 is zero of this polynomial, and another factor is Use this information to factor the polynomial completely Fundamental Theorem

Fundamental Theorem

Fundamental Theorem

Pg 140 – 141 11, 14, 19, 22, 25, 29, 30, 32, 35, 48, 53, 54 Homework