Division Algorithm for Polynomials - Explanation with Example - Teacho

Division Algorithm for Polynomials - Part 2
Division Algorithm for Polynomials - Part 3 Division Algorithm for Polynomials - Part 4 Division Algorithm for Polynomials - Part 5

 

Let us first divide 7 by 3,

7/3

Division Algorithm for Polynomials - Part 6

 

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

Division Algorithm for Polynomials - Part 7

 

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

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Transcript

Dividing two numbersQuotient Divisor Dividend Remainder Which can be rewritten as a sum like this: Division Algorithm is Dividend = Divisor × Quotient + Remainder Quotient Divisor Dividend Remainder Dividing two Polynomials Let’s divide 3x2 + x − 1 by 1 + x We can write Dividend = Divisor × Quotient + Remainder 3x2 + x – 1 = (x + 1) (3x – 2) + 1 What if…We don’t divide? We divide 3x2 + x − 1 by x + 1 So, Dividend = Divisor × Quotient + Remainder 3x2 + x – 1 = (x + 1) × Quotient + Remainder Putting x = −1 3(−1)2 + (−1) – 1 = (−1 + 1) × Quotient + Remainder 1 = Remainder Remainder = 1

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.