Polynomial Division

1
Polynomial Division
2
Basic Idea about Division

• There is an inverse relationship between
  Multiplication and Division
• If 7x321 then 2173
• Let us first look how we normally multiply
  polynomials in order to understand how we will
  divide them.

3
Polynomial Multiplication Area Method
Multiply (x 5)(x2 4x 1)



x2
-4x
1
We will reverse this process to divide
polynomials!
x
x3
-4x2
x
5
5x2
-20x
5
x3
x2
19x
5
4
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.

5
Polynomial Division Area Method
Divide x4 10x2 2x 3 by x 3
Quotient



x3
3x2
-x
-1
Dividend (make sure to include all powers of x)
x
x4
3x3
-x2
-x
The sum of these boxes must be the dividend
Divisor
- 3
-3x3
-9x2
3x
3
x4 0x3 10x2 2x 3
Needed
Needed
Needed
Check
Needed
x3 3x2 x 1
6
Polynomial Division
Divide 6x3 7x2 16x 18 by 2x 5



3x2
-4x
2
Rm
2x
6x3
-8x2
4x
8
5
15x2
-20x
10
6x3 7x2 16x 18