翰林提供学术活动、国际课程、科研项目一站式留学背景提升服务!
400 888 0080
首页
国际少培课程
CogAT认知能力测试
国际课程
A-Level课程辅导
IB课程辅导
AP课程辅导
IGCSE课程辅导
美高课程辅导
国际竞赛
理科国际竞赛
商科国际竞赛
STEM科创竞赛
文社科国际竞赛
丘成桐中学生科学奖
热门资讯
学校动态
赛事动态
课程动态
真题资料
关于我们
学员奖项
2024-至今年度奖项
2022-2023年度奖项
2020-2021年度奖项
翰林导师
加入我们
商务合作
Home
»
国际课程
»
IB课程
»
Details
IB DP Maths: AA HL复习笔记2.7.1 Factor & Remainder Theorem
Category:
IB课程
,
教材笔记
,
福利干货
Date: 2022年7月12日 上午11:17
What is the factor theorem?
The
factor theorem
is used to find the linear factors of
polynomial
equations
This topic is closely tied to finding the
zeros
and
roots
of a
polynomial
function/equation
As a rule of thumb a
zero
refers to the polynomial function and a
root
refers to a polynomial equation
For any
polynomial
function
P
(
x
)
(
x
-
k
) is a
factor
of
P
(
x
) if
P
(
k
) = 0
P
(
k
) = 0
if (
x
-
k
) is a
factor
of
P
(
x
)
How do I use the factor theorem?
Exam Tip
A common mistake in exams is using the incorrect sign for either the root or the factor
If you are asked to find integer solutions to a polynomial then you only need to consider factors of the constant term
Worked Example
Remainder Theorem
What is the remainder theorem?
The
remainder theorem
is used to find the remainder when we divide a
polynomial
function by a linear function
When any polynomial
P
(
x
) is divided by any linear function (
x
-
k
) the value of the remainder
R
is given by
P
(
k
) =
R
Note, when
P
(
k
) = 0 then (
x
-
k
) is a factor of
P
(
x
)
How do I use the remainder theorem?
Consider the polynomial function
P
(
x
) =
a
n
x
n
+
a
n-1
x
n
-1
+ … +
a
1
x
+
a
0
and the linear function (
x - k
)
Then, due to the remainder theorem
P
(
k
) =
a
n
k
n
+
a
n-1
k
n
-1
+ … +
a
1
k
+
a
0
=
R
Worked Example
转载自savemyexams
Previous post: Edexcel IGCSE Biology 复习笔记 5.1.4 Anaerobic Respiration in Yeast
Next post: IB DP Maths: AA HL复习笔记2.7.2 Polynomial Division
2024年AMC数学竞赛报名开启!
CNEC挑战赛报名启动!点击咨询!
站内搜索
在线登记
最新发布
A-level文科生从选课到申请学校专业攻略!
IGCSE课程是否有必修课程?如何按专业选择课程?
为什么要选IB物理?IB物理考察内容是什么?
2025年伦敦新人文学院写作竞赛即将开题!请于1月6日前提交作品!
2024年耶鲁青年诗人系列奖比赛即将开赛!一文了解参赛规则!
A-Level还是高考:你要怎么选择?
预告!哈佛Crimson全球写作比赛(HCGEC)报名即将开启!
AP课程与美高的不同
热门标签
AMC
物理碗
AMC8
BBO
AMC10
欧几里得数学竞赛
Physics Bowl
John Locke
AMC12
USABO
USACO
PhysicsBowl
AIME
袋鼠数学竞赛
NEC
BPhO
AP
丘成桐中学科学奖
欧几里得
HiMCM美国高中数学建模竞赛
UKChO
SIC
Euclid
Brain bee
IEO
© 2024. All Rights Reserved.
沪ICP备2023009024号-1
国际竞赛
了解背提项目
国际课程
商务合作
Go to top