This PowerPoint helps students to consider the concept of infinity.
Pc 2.5 a_notes
1. 2.5 Zeros of
Polynomial Functions
Essential 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
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Linear Factorization Theorem:
If f(x) is a polynomial of degree n, where
n > 0, then f has precisely n linear factors
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where c1, c2, ... c n are complex numbers.
3. Ex. 1) Find all zeros and write the linear factorization of the
function.
4.
5. Please note:
FTA (fundamental theorem of algebra) and LFT (linear
factorization theorem) only tell us that zeros exist, not how
to find them.
Methods for finding zeros:
6. Rational Zero Test
If the polynomial f(x) has __________
coefficients, every rational zero of f has the
form:
Where _____ and _____ have no common
factors other than 1 and
______ = a factor of the _____________
______ = a factor of the _____________
