Factor Theorem - Checking if Factor

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.