Post on 03-Jan-2016
Remainder Theorem
Long Division
Long Division QuestionDivide the following
)3(524 23 xxxx
Long Division
5243 23 xxxx
How many times does x go into x3 ?2x Multiply x-3 by x2 .
23 3xx
Subtract down. Note 4x2 – (-3x2)=4x2 + (+3x2)=7x2
27x
Bring down +2x.
x2How many times does x go into 7x2 ?
x7
xx 217 2 Multiply x-3 by 7x.Subtract down.
x23 5 Bring down –5.How many times does x go into 23x ?
23
Multiply x-3 by 23.6923 x
Subtract down.64
See textbook pg 85 for Computer Algebra System division
Synthetic Division
3 1 4 2 -5
1
3
7
21
23
69
6464)237)(3(524 223 xxxxxxThe division statement is:
To find the remainder without doing the division we could substitute 3 into the function.
You try one (see Notebook)
Remainder Theorem•When a function f(x), is divided by x – k
•the remainder is f(k)
Example 1
1 x b)
2- x a)
by divided is
362when xremainder theDetermine 23
xx
362x)(Let a) 23 xxxf
3)2(6)2(2(2))2( 23 f
153128-8)2( f
15. isremainder theSo
362x)(Let b) 23 xxxf
3)1(6)1(2(-1))1( 23 f-636-2--1)1( f
6.- isremainder theSo
Example 2
. of value theFind 3. isremainder the
2)-(xby divided is 74When 23
m
xmxx
74 )(Let
:Solution23 xmxxxf
7)2(4)2()2( )2(
3)2( that states theoremremainder The23
mf
f
7848 )2( mf
234 )2( mf
3234
3 )2(Set
m
f
5m