Difference between revisions of "Factor Theorem"
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Revision as of 13:04, 14 July 2021
The Factor Theorem says that if is a polynomial, then
is a factor of
if
.
Proof
If is a factor of
, then
, where
is a polynomial with
. Then
.
Now suppose that .
Apply Remainder Theorem to get , where
is a polynomial with
and
is the remainder polynomial such that
. This means that
can be at most a constant polynomial.
Substitute and get
. Since
is a constant polynomial,
for all
.
Therefore, , which shows that
is a factor of
.
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