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Polynomials Integrated Math 4 Mrs. Tyrpak

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Definition

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Key Terms

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You try one…

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Relationships?

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The Leading Coefficient Test L.C. EVEN ODD Same Different L.C. DEGREE

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Real Zeros The following are equivalent statements about real zeros of a polynomial function: 1.x = a is a zero (solution or root) of the function 2.(a, 0) is an x-intercept of the graph 3.(x – a) is a factor of the polynomial

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Finding All Zeros

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Rational Zeros Theorem

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Synthetic Division Second, we are going to use synthetic division to test each possible zero.

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The Remainder and Factor Theorems Remainder Theorem: If a polynomial f(x) is divided by x – k, the remainder is r = f(k). Factor Theorem: A polynomial f(x) has a factor (x - k) if and only if f(k)=0.

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Factor the Polynomial

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Find all the zeros Lastly, we will solve each factor for each zero.

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Fundamental Theorem of Algebra If f(x) is a polynomial of degree n, where n > 0, f has at least one zero in the complex number system.

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Multiplicity

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Find the zeros of the polynomial function and state the multiplicity of each and what happens at each zero.

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Finding All Zeros and Factors

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Take 5 minutes and try this one..

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Let’s try and work backwards Find a polynomial with integer coefficients that has the given zeros: 1, 5i, -5i

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Thanks for your attention! Don’t forget to complete both the extension and enrichment assignments before you move on. Keep up the hard work!

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