200
L19
Zeros of a Polynomial Function
Division Algorithm for Polynomials
If
f
and
g
are two polynomials and
g
is not the
zero polynomial, then there are the unique
polynomials
q
(quotient) and
r
(remainder) such
that
( )
( )
( )
( )
( )
f x
r x
q x
g x
g x
=
+
or
( )
( )
( )
( )
f x
q x g x
r x
=
+
where ( )
r x
either the zero polynomial or of degree
less than the degree of
( )
g x
.
Note
:
If
( )
g x
x
c
=
−
, then
( )
( )(
)
f x
q x
x
c
r
=
−
+
,
where
r
is a number.
If
x
c
=
, then
( )
f c
=
Remainder Theorem
If a polynomial
( )
f x
is divided by (
)
x
c
−
, then the
remainder
( )
r
f c
=
.

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