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

Finding Remainder using  long division - Dividing two polynomials.jpg

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

  1. Chapter 2 Class 9 Polynomials
  2. Concept wise
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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.