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- 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. 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. Ex. 1) Find all zeros and write the linear factorization of thefunction.
- 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. 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. Ex. 2) Find the rational zeros of
- 7. Ex. 3) Find the rational zeros of
- 8. Ex. 4) Find all the real solutions of
- 9. Whats the difference?Find all rational zeros:Find all real zeros:Find all zeros:
- 10. Conjugate PairsIf ___________ is a zero of thefunction, then ___________ is also azero of the function.
- 11. Ex. 5) Find a fourth-degree polynomial with realcoefficients that has 3+2i and 4-i as zeros.
- 12. Assignment:2.5A p. 179#7-19 (odd),37, 39, 41

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