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.