![Division Algorithm for Polynomials - Part 2](https://d1avenlh0i1xmr.cloudfront.net/fa80c5b3-1dbf-4569-bf76-2d450871f1d7/slide3.jpg)
![Division Algorithm for Polynomials - Part 3](https://d1avenlh0i1xmr.cloudfront.net/d38f3a15-708d-4f67-bde9-f57b17f5a6ed/slide4.jpg)
![Division Algorithm for Polynomials - Part 4](https://d1avenlh0i1xmr.cloudfront.net/9b91bed3-1743-4a19-a71b-ce70a4150d5f/slide5.jpg)
![Division Algorithm for Polynomials - Part 5](https://d1avenlh0i1xmr.cloudfront.net/0ca48246-70bd-4ede-be96-a66f74d7a09d/slide6.jpg)
Let us first divide 7 by 3,
7/3
Here
7 = 3 × 2 + 1
i.e. Dividend = Divisor × Quotient + Remainder
We can do the same when dividing two polynomials
In Example 6 ,
We divided 3x 2 + x − 1 by 1 + x
Our division was
Here
Dividend = 3x 2 + x – 1
Divisor = x + 1
Quotient = 3x – 2
And Remainder = 1
Dividend = Divisor × Quotient + Remainder
3x 2 + x – 1 = (x + 1) (3x – 2) + 1
3x 2 + x – 1 = x (3x – 2) + 1 (3x – 2) + 1
3x 2 + x – 1 = 3x 2 – 2x + 3x – 2 + 1
3x 2 + x – 1 = 3x 2 + x – 1