1. Polynomial Division

2. 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.

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
Divisor
The sum of these boxes must be the dividend
- 3
-3x3
-9x2 3x 3
x x3 –10x2 +2x
Needed
Needed
Needed
Needed
Check
x3 + 3x2 – x – 1

6. Polynomial Division 3x2 -4x 2 Rm 2x 6x3 -8x2 4x 8 + 5 15x2 -20x 10
Divide 6x3 + 7x2 – 16x + 18 by 2x + 5
3x2
-4x 2 Rm 2x
6x3
-8x2 4x 8
+ 5
15x2
-20x 10
6x x2 – 16x