Transcript Polynomial Division

Polynomial Division
Basic Idea about Division
There is an inverse relationship between
Multiplication and Division:
If 7x3=21 then 21÷7=3
Let us first look how we normally multiply
polynomials in order to understand how
we will divide them.
Polynomial Multiplication: Area
Method
Multiply (x + 5)(x2 – 4x + 1)
x2
-4x
3
2
+1
x
x
-4x
x
+5
5x2
-20x
5
x3
+ x2 – 19x
+5
We will reverse
this process to
divide
polynomials!
Basic Idea about Division
Now reverse the process.
This time you will know the final answer and
only one of the factors. You will need to
use the area method to find the missing
factor.
Polynomial Division: Area Method
Divisor
Divide x4 – 10x2 + 2x + 3 by x – 3
Quotient
x
x3
3x2
-x
-1
4
3
2
-x
x
3x
-x
The sum of these boxes must be
the dividend
-3
-3x3
x4
+0x3 –10x2 +2x
+3
3 Needed2
Check
Needed
Needed
-9x2
3x
Needed
x + 3x – x – 1
3
Dividend
(make
sure to
include
all
powers
of x)
Polynomial Division
Divide 6x3 + 7x2 – 16x + 18 by 2x + 5
3x2
3
-4x
2
Rm
2
8
2x
6x
-8x
4x
+5
15x2
-20x
10
6x3 + 7x2 – 16x + 18
3x  4 x  2 
2
8
2 x 5