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Remainder of Polynomial Division
Toolkit 32
Remainder of Polynomial Division
A
(
x
)
÷
B
(
x
)
:
A
(
x
)
=
B
(
x
)
Q
(
x
)
+
R
(
x
)
,
deg
(
R
(
x
)
)
<
deg
(
B
(
x
)
)
A(x)\div B(x):\;A(x)=B(x)Q(x)+R(x),\quad \deg(R(x))<\deg(B(x))
A
(
x
)
÷
B
(
x
)
:
A
(
x
)
=
B
(
x
)
Q
(
x
)
+
R
(
x
)
,
de
g
(
R
(
x
))
<
de
g
(
B
(
x
))
⇒
If
B
(
x
)
=
0
,
then
A
(
x
)
=
R
(
x
)
\Rightarrow\text{ If }B(x)=0,\text{ then }A(x)=R(x)
⇒
If
B
(
x
)
=
0
,
then
A
(
x
)
=
R
(
x
)
Related Problems
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AMC 10B 2022 (Problem 21)
AMC 12A 2022 (Problem 21)
AMC 12B 2021 Spring (Problem 20)
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