How to check a factor using Factor Theorem? - Class 9 Teachoo

Factor Theorem - Checking if Factor - Part 2
Factor Theorem - Checking if Factor - Part 3 Factor Theorem - Checking if Factor - Part 4 Factor Theorem - Checking if Factor - Part 5

 

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.

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Davneet Singh

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.