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A rational function
(polynomial) is a function of
the form:
n
n 1
P( x)  a0 x  a1x 
...


The root of a polynomial is the
value of the argument x=x0, at
which the polynomial is zero
...

Each polynomial is decomposed
into simple linear and simple
quadratic factors as follows:

P(x)  (x  x1 )
...
( x  pm x  qm )
k1

Real root
Linear
multipliers with
multiplicity ki

kr

Two complex
conjugate
roots

Square
multipliers with
multiplicity si

Each multiplier
corresponds to:

1
...


2
...


3
...


Polynomial of degree 9 is
given:

P(x)  (x  2x  x)(x  8x  25)
3

2

2

Find the roots of a polynomial,
determine their multiplicity,
decompose the polynomial
into prime factors

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