Remainder Theorem

Last updated at April 16, 2024 by

Remainder Theorem for Polynomials (Why is it used + Examples) - Teacho

Remainder Theorem - Part 2
Remainder Theorem - Part 3

Let us find remainder when p(x) is divided by g(x)

p(x) = x 3 − 3x 2   + 4x + 10

g(x) = x + 1

 

By Long Division

Remainder Theorem - Part 4

So, Remainder = 2

There is another method to find remainder by Remainder Theorem

Remainder Theorem

 

In remainder theorem

  1. We put g(x) = 0, and find x.
  2. Let x = a
  3. Put a in p(x)
  4. Remainder = p(a)

 

So, in our example

If  p(x) = x 3 − 3x 2   + 4x + 10 is divided by g(x) = x + 1

 

Putting g(x) = 0

        x + 1 = 0

           x =  − 1

 

  So, Remainder = p(−1)

    = (−1) 3   − 3(−1) 2 + 4(−1) + 10

    = (−1)  − 3 × 1  − 4 + 10

    = −1 − 3 − 4 + 10

    = 2

 

So, Remainder = 2

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 PolynomialsLet’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 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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.