To check if g(x) is a factor of p(x),

If on dividing p(x) by g(x), we get remainder 0,

Then g(x) is a factor of p(x)

 

Let us take an example

p(x) = x 3 − 3x 2   + 4x + 10

g(x) = x + 1

 

Is g(x) a factor of p(x)?

 

We find remainder by Remainder theorem

Putting g(x) = 0 

        x + 1 = 0

           x =  − 1

 

So, Remainder = p(− 1)

    = (−1) 3   − 3(− 1) 2 + 4(−1) + 10

    = (−1)  − 3 x 1  − 4 + 10

    = −1 − 3 − 4 + 10

    = 2

 

Since Remainder ≠ 0

It is not a factor.

 

Let us check more examples. click next to practice more questions.

  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.