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Pc 2.5 a_notes

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Pc 2.5 a_notes

1. 1. 2.5 Zeros ofPolynomial FunctionsEssential Questions:1) How do you find the zeros of a polynomial function?2) What is the rational zero test?
2. 2. The Fundamental Theorem of Algebra: If f(x) is a polynomial of degree n, where n > 0, then f has at least one zero in the ______________________________Linear Factorization Theorem: If f(x) is a polynomial of degree n, where n > 0, then f has precisely n linear factors ______________________________ where c1, c2, ... c n are complex numbers.
3. 3. Ex. 1) Find all zeros and write the linear factorization of thefunction.
4. 4. Please note:FTA (fundamental theorem of algebra) and LFT (linearfactorization theorem) only tell us that zeros exist, not howto find them. Methods for finding zeros:
5. 5. Rational Zero TestIf the polynomial f(x) has __________coefficients, every rational zero of f has theform:Where _____ and _____ have no commonfactors other than 1 and______ = a factor of the ___________________ = a factor of the ____________­_
6. 6. Ex. 2) Find the rational zeros of
7. 7. Ex. 3) Find the rational zeros of
8. 8. Ex. 4) Find all the real solutions of
9. 9. Whats the difference?Find all rational zeros:Find all real zeros:Find all zeros:
10. 10. Conjugate PairsIf ___________ is a zero of thefunction, then ___________ is also azero of the function.
11. 11. Ex. 5) Find a fourth-degree polynomial with realcoefficients that has 3+2i and 4-i as zeros.
12. 12. Assignment:2.5A p. 179#7-19 (odd),37, 39, 41